UPSC IES And ISS Syllabus 2023
The Union Public Service Commission (UPSC) conducts the Indian Economic Service (IES) and Indian Statistical Service (ISS) Examination every year.
The IES exam is held to recruit candidates for various economic posts in government departments and organizations. Candidates who have a postgraduate degree in Economics, Applied Economics, Business Economics, Econometrics, or equivalent from a recognized university can apply for this exam.
The ISS exam is held to recruit candidates for various statistical posts in government departments and organizations. Candidates who have a bachelor's degree with Statistics/Mathematical Statistics/Applied Statistics as one of the subject or a Master's degree in Statistics/Mathematical Statistics/Applied Statistics can apply for this exam.
The selection process for both exams consists of a written examination followed by an interview. The written examination consists of two stages - a preliminary examination and a main examination.
The preliminary examination is objective in nature and consists of multiple-choice questions. The main examination is a descriptive type of exam and consists of conventional essay-type questions.
Candidates who qualify in the written examination are called for an interview, which is conducted to assess their personality and suitability for the job.
The IES and ISS examination is considered to be one of the most competitive exams in India. To crack this exam, candidates need to have a strong understanding of economics and statistics, as well as excellent analytical and problem-solving skills. It is important for candidates to start their preparation early and have a structured study plan in place.
संघ लोक सेवा आयोग (यूपीएससी) हर साल भारतीय आर्थिक सेवा (आईईएस) और भारतीय सांख्यिकी सेवा (आईएसएस) परीक्षा आयोजित करता है।
सरकारी विभागों और संगठनों में विभिन्न आर्थिक पदों के लिए उम्मीदवारों की भर्ती के लिए IES परीक्षा आयोजित की जाती है। जिन उम्मीदवारों के पास किसी मान्यता प्राप्त विश्वविद्यालय से अर्थशास्त्र, एप्लाइड इकोनॉमिक्स, बिजनेस इकोनॉमिक्स, इकोनोमेट्रिक्स या समकक्ष में स्नातकोत्तर डिग्री है, वे इस परीक्षा के लिए आवेदन कर सकते हैं।
सरकारी विभागों और संगठनों में विभिन्न सांख्यिकीय पदों के लिए उम्मीदवारों की भर्ती के लिए आईएसएस परीक्षा आयोजित की जाती है। जिन उम्मीदवारों के पास एक विषय के रूप में सांख्यिकी/गणितीय सांख्यिकी/अनुप्रयुक्त सांख्यिकी के साथ स्नातक की डिग्री है या सांख्यिकी/गणितीय सांख्यिकी/अनुप्रयुक्त सांख्यिकी में मास्टर डिग्री है, वे इस परीक्षा के लिए आवेदन कर सकते हैं।
दोनों परीक्षाओं के लिए चयन प्रक्रिया में एक लिखित परीक्षा होती है जिसके बाद एक साक्षात्कार होता है। लिखित परीक्षा में दो चरण होते हैं - एक प्रारंभिक परीक्षा और एक मुख्य परीक्षा।
प्रारंभिक परीक्षा वस्तुनिष्ठ प्रकृति की होती है और इसमें बहुविकल्पीय प्रश्न होते हैं। मुख्य परीक्षा एक वर्णनात्मक प्रकार की परीक्षा है और इसमें पारंपरिक निबंध-प्रकार के प्रश्न होते हैं।
लिखित परीक्षा में अर्हता प्राप्त करने वाले उम्मीदवारों को साक्षात्कार के लिए बुलाया जाता है, जो नौकरी के लिए उनके व्यक्तित्व और उपयुक्तता का आकलन करने के लिए आयोजित किया जाता है।
IES और ISS परीक्षा को भारत में सबसे अधिक प्रतिस्पर्धी परीक्षाओं में से एक माना जाता है। इस परीक्षा को क्रैक करने के लिए, उम्मीदवारों को अर्थशास्त्र और सांख्यिकी की मजबूत समझ के साथ-साथ उत्कृष्ट विश्लेषणात्मक और समस्या को सुलझाने के कौशल की आवश्यकता होती है। उम्मीदवारों के लिए यह महत्वपूर्ण है कि वे अपनी तैयारी जल्दी शुरू करें और एक संरचित अध्ययन योजना तैयार करें।
What are the Mode of selection UPSC IES & ISS Recruitment 2023 ?
Written Examination (Part-1 & Part2)
Interview/Personality Test
SCHEME OF EXAMINATION SECTION-I
The examination shall be conducted according to the following plan—
Part I-Written examination carrying a maximum of 1000 marks in the subjects as shown below.
Part II-Viva voce of such candidates as may be called by the Commission carrying a maximum of 200 marks.
PART-I
The subjects of the written examination under Part-I, the maximum marks allotted to each subject/paper and the time allowed shall be as follows :
A. Indian Economic Service
Sl. No. / Subject / Maximum Marks / Time Allowed
1. General English 100 3 hrs.
2. General Studies 100 3 hrs.
3. General Economics-I 200 3 hrs.
4. General Economics-II 200 3 hrs.
5. General Economics-III 200 3 hrs.
6. Indian Economics 200 3 hrs.
B. Indian Statistical Service
Sl. No. / Subject / Maximum Marks / Time Allowed
1. General English 100 3 hrs.
2. General Studies 100 3 hrs.
3. Statistics-I (Objective) 200 2 hrs.
4. Statistics-II (Objective) 200 2 hrs.
5. Statistics-III (Descriptive) 200 3 hrs.
6. Statistics-IV (Descriptive) 200 3 hrs.
Note-1: Statistics I & II will be of Objective Type Questions (80 questions with maximum marks
of 200 in each paper) to be attempted in 120 minutes.
Note-2: Statistics III and IV will be of Descriptive Type having Short Answer/ Small Problems
Questions (50%) and Long Answer and Comprehension problem questions (50%). At
least one Short Answer and One Long Answer Question from each section is
compulsory. In Statistics-IV, there will be SEVEN Sections in the paper. Candidates
have to choose any TWO Sections out of them. All Sections will carry equal marks.
Note-3: The papers on General English and General Studies, common to both Indian Economic
Service and Indian Statistical Service will be of subjective type.
Note-4: All other papers of Indian Economic Service will be of subjective type.
Note-5: The details of standard and syllabi for the examination are given in Section-II below
PART - II
Viva voce—The candidate will be interviewed by a Board of competent and unbiased
observers who will have before them a record of his/her career. The object of the interview
is to assess his/her suitability for the service for which he/she has competed. The interview
is intended to supplement the written examination for testing the general and specialised
knowledge and abilities for the candidate. The candidate will be expected to have taken an
intelligent interest not only in his/her subjects of academic study but also in events which
are happening around him/her both within and outside his/her own State or Country as
well as in modern currents of thought and in new discoveries which should rouse the
curiosity of well educated youth.
The technique of the interview is not that of a strict cross-examination, but of a
natural, through directed and purposive conversation intended to reveal the candidate's
mental qualities and his/her grasp of problems. The Board will pay special attention to
assess the intellectual curiosity, critical powers of assimilation, balance of judgment and
alertness of mind, the ability for social cohesion, integrity of character initiative and
capacity for leadership.
SECTION-II
STANDARD AND SYLLABI
The standard of papers in General English and General Studies will be such as may be
expected of a graduate of an Indian University.
The standard of papers in the other subjects will be that of the Master’s degree
examination of an Indian University in the relevant disciplines. The candidates will be
expected to illustrate theory by facts, and to analyse problems with the help of theory. They
will be expected to be particularly conversant with Indian problems in the field(s) of
Economics/Statistics.
GENERAL ENGLISH (COMM0N TO BOTH IES/ISS)
Candidates will be required to write an essay in English. Other questions will be
designed to test their understanding of English and workman like use of words. Passages
will usually be set for summary or precis.
GENERAL STUDIES (COMM0N TO BOTH IES/ISS)
General knowledge including knowledge of current events and of such matters of
everyday observation and experience in their scientific aspects as may be expected of an
educated person who has not made a special study of any scientific subject. The paper will
also include questions on Indian Polity including the political system and the Constitution
of India, History of India and Geography of a nature which a candidate should be able to
answer without special study
GENERAL ECONOMICS – I (For IES only)
PART A :
1. Theory of Consumer’s Demand—Cardinal utility Analysis: Marginal utility and
demand, Consumer’s surplus, Indifference curve Analysis and utility function, Price,
income and substitution effects, Slutsky theorem and derivation of demand curve, Revealed
preference theory. Duality and indirect utility function and expenditure function, Choice
under risk and uncertainty. Simple games of complete information, Concept of Nash
equilibrium.
2. Theory of Production: Factors of production and production function. Forms of
Production Functions: Cobb Douglas, CES and Fixed coefficient type, Translog production
function. Laws of return, Returns to scale and Return to factors of production. Duality and
cost function, Measures of productive efficiency of firms, technical and allocative efficiency.
Partial Equilibrium versus General Equilibrium approach. Equilibrium of the firm and
industry.
3. Theory of Value: Pricing under different market structures, public sector pricing,
marginal cost pricing, peak load pricing, cross-subsidy free pricing and average cost pricing.
Marshallian and Walrasian stability analysis. Pricing with incomplete information and
moral hazard problems.
4. Theory of Distribution: Neo classical distribution theories; Marginal productivity theory
of determination of factor prices, Factor shares and adding up problems. Euler’s theorem,
Pricing of factors under imperfect competition, monopoly and bilateral monopoly. Macrodistribution theories of Ricardo, Marx, Kaldor, Kalecki.
5. Welfare Economics: Inter-personal comparison and aggression problem, Public goods
and externalities, Divergence between social and private welfare, compensation principle.
Pareto optimality. Social choice and other recent schools, including Coase and Sen.
PART B : Quantitative Methods in Economics
1. Mathematical Methods in Economics: Differentiation and Integration and their
application in economics. Optimisation techniques, Sets, Matrices and their application in
economics. Linear algebra and Linear programming in economics and Input-output model
of Leontief.
2. Statistical and Econometric Methods: Measures of central tendency and
dispersions, Correlation and Regression. Time series. Index numbers. Sampling of curves
based on various linear and non-linear function. Least square methods and other
multivariate analysis (only concepts and interpretation of results). Analysis of Variance,
Factor analysis, Principle component analysis, Discriminant analysis. Income distribution:
Pareto law of Distribution, lognormal distribution, measurement of income inequality.
Lorenz curve and Gini coefficient. Univariate and multivariate regression analysis. Problems
and remedies of Hetroscedasticity, Autocorrelation and Multicollnearity.
GENERAL ECONOMICS – II (For IES only)
1. Economic Thought: Mercantilism Physiocrats, Classical, Marxist, Neo-classical,
Keynesian and Monetarist schools of thought.
2. Concept of National Income and Social Accounting: Measurement of National
Income, Inter relationship between three measures of national income in the presence of
Government sector and International transactions. Environmental considerations, Green
national income.
3. Theory of employment, Output, Inflation, Money and Finance: The Classical
theory of Employment and Output and Neo classical approaches. Equilibrium, analysis
under classical and neo classical approach. Keynesian theory of Employment and Output.
Post Keynesian developments. The inflationary gap; Demand pull versus cost push
inflation, the Philip’s curve and its policy implication. Classical theory of Money, Quantity
theory of Money. Friedman’s restatement of the quantity theory, the neutrality of money.
The supply and demand for loanable funds and equilibrium in financial markets, Keynes’
theory on demand for money. IS-LM Model and AD-AS Model in Keynesian Theory.
4. Financial and Capital Market: Finance and economic development, financial
markets, stock market, gilt market, banking and insurance. Equity markets, Role of
primary and secondary markets and efficiency, Derivatives markets; Future and options.
5. Economic Growth and Development: Concepts of Economic Growth and
Development and their measurement: characteristics of less developed countries and
obstacles to their development – growth, poverty and income distribution. Theories of
growth: Classical Approach: Adam Smith, Marx and Schumpeter- Neo classical approach;
Robinson, Solow, Kaldor and Harrod Domar. Theories of Economic Development, Rostow,
Rosenstein-Roden, Nurske, Hirschman, Leibenstien and Arthur Lewis, Amin and Frank
(Dependency school) respective role of state and the market. Utilitarian and Welfarist
approach to social development and A.K. Sen’s critique. Sen’s capability approach to
economic development. The Human Development Index. Physical quality of Life Index and
Human Poverty Index. Basics of Endogenous Growth Theory.
6. International Economics: Gains from International Trade, Terms of Trade, policy,
international trade and economic development- Theories of International Trade; Ricardo,
Haberler, Heckscher- Ohlin and Stopler- Samuelson- Theory of Tariffs- Regional Trade
Arrangements. Asian Financial Crisis of 1997, Global Financial Crisis of 2008 and Euro
Zone Crisis- Causes and Impact.
7. Balance of Payments: Disequilibrium in Balance of Payments, Mechanism of
Adjustments, Foreign Trade Multiplier, Exchange Rates, Import and Exchange Controls and
Multiple Exchange Rates. IS-LM Model and Mundell- Fleming Model of Balance of
Payments.
8. Global Institutions: UN agencies dealing with economic aspects, role of Multilateral
Development Bodies (MDBs), such as World Bank, IMF and WTO, Multinational
Corporations. G-20.
GENERAL ECONOMICS – III (For IES only)
1. Public Finance—Theories of taxation: Optimal taxes and tax reforms, incidence of
taxation. Theories of public expenditure: objectives and effects of public expenditure, public
expenditure policy and social cost benefit analysis, criteria of public investment decisions,
social rate of discount, shadow prices of investment, unskilled labour and foreign exchange.
Budgetary deficits. Theory of public debt management.
2. Environmental Economics—Environmentally sustainable development, Rio process
1992 to 2012, Green GDP, UN Methodology of Integrated Environmental and Economic
Accounting. Environmental Values: Users and Non-Users values, option value. Valuation
Methods: Stated and revealed preference methods. Design of Environmental Policy
Instruments: Pollution taxes and Pollution permits, collective action and informal regulation
by local communities. Theories of exhaustible and renewable resources. International
environmental agreements, RIO Conventions. Climatic change problems. Kyoto protocol,
UNFCC, Bali Action Plan, Agreements up to 2017, tradable permits and carbon taxes.
Carbon Markets and Market Mechanisms. Climate Change Finance and Green Climate
Fund.
3. Industrial Economics—Market structure, conduct and performance of firms, product
differentiation and market concentration, monopolistic price theory and oligopolistic
interdependence and pricing, entry preventing pricing, micro level investment decisions and
the behaviour of firms, research and development and innovation, market structure and
profitability, public policy and development of firms.
4. State, Market and Planning—Planning in a developing economy. Planning regulation
and market. Indicative planning. Decentralised planning.
INDIAN ECONOMICS (For IES only)
1. History of development and planning— Alternative development strategies—goal
of self-reliance based on import substitution and protection, the post-1991 globalisation
strategies based on stabilisation and structural adjustment packages: fiscal reforms,
financial sector reforms and trade reforms.
2. Federal Finance—Constitutional provisions relating to fiscal and financial powers of
the states, Finance Commissions and their formulae for sharing taxes, Financial aspect of
Sarkaria Commission Report, Financial aspects of 73rd and 74th Constitutional
Amendments.
3. Budgeting and Fiscal Policy—Tax, expenditure, budgetary deficits, pension and
fiscal reforms, Public debt management and reforms, Fiscal Responsibility and Budget
Management (FRBM) Act, Black money and Parallel economy in India—definition,
estimates, genesis, consequences and remedies.
4. Poverty, Unemployment and Human Development—Estimates of inequality and
poverty measures for India, appraisal of Government measures, India’s human development
record in global perspective. India’s population policy and development.
5. Agriculture and Rural Development Strategies— Technologies and institutions,
land relations and land reforms, rural credit, modern farm inputs and marketing— price
policy and subsidies; commercialisation and diversification. Rural development programmes
including poverty alleviation programmes, development of economic and social
infrastructure and New Rural Employment Guarantee Scheme.
6. India’s experience with Urbanisation and Migration—Different types of migratory
flows and their impact on the economies of their origin and destination, the process of
growth of urban settlements; urban development strategies.
7. Industry: Strategy of industrial development— Industrial Policy Reform;
Reservation Policy relating to small scale industries. Competition policy, Sources of
industrial finance. Bank, share market, insurance companies, pension funds, non-banking
sources and foreign direct investment, role of foreign capital for direct investment and
portfolio investment, Public sector reform, privatisation and disinvestment.
8. Labour—Employment, unemployment and underemployment, industrial relations
and labour welfare— strategies for employment generation—Urban labour market and
informal sector employment, Report of National Commission on Labour, Social issues
relating to labour e.g. Child Labour, Bonded Labour International Labour Standard and its
impact.
9. Foreign trade—Salient features of India’s foreign trade, composition, direction and
organisation of trade, recent changes in trade, balance of payments, tariff policy, exchange
rate, India and WTO requirements. Bilateral Trade Agreements and their implications.
10. Money and Banking—Financial sector reforms, Organisation of India’s money
market, changing roles of the Reserve Bank of India, commercial banks, development
finance institutions, foreign banks and non-banking financial institutions, Indian capital
market and SEBI, Development in Global Financial Market and its relationship with Indian
Financial Sector. Commodity Market in India-Spot and Futures Market, Role of FMC.
11. Inflation—Definition, trends, estimates, consequences and remedies (control):
Wholesale Price Index. Consumer Price Index: components and trends.
STATISTICS-I (OBJECTIVE TYPE) (For ISS only)
(i) Probability:
Classical and axiomatic definitions of Probability and consequences. Law of total
probability, Conditional probability, Bayes' theorem and applications. Discrete and
continuous random variables. Distribution functions and their properties.
Standard discrete and continuous probability distributions - Bernoulli, Uniform, Binomial,
Poisson, Geometric, Rectangular, Exponential, Normal, Cauchy, Hyper geometric,
Multinomial, Laplace, Negative binomial, Beta, Gamma, Lognormal. Random vectors, Joint
and marginal distributions, conditional distributions, Distributions of functions of random
variables. Modes of convergences of sequences of random variables - in distribution, in
probability, with probability one and in mean square. Mathematical expectation and
conditional expectation. Characteristic function, moment and probability generating
functions, Inversion, uniqueness and continuity theorems. Borel 0-1 law, Kolmogorov's 0-1
law. Tchebycheff's and Kolmogorov's inequalities. Laws of large numbers and central limit
theorems for independent variables.
(ii) Statistical Methods:
Collection, compilation and presentation of data, charts, diagrams and histogram.
Frequency distribution. Measures of location, dispersion, skewness and kurtosis. Bivariate
and multivariate data. Association and contingency. Curve fitting and orthogonal
polynomials. Bivariate normal distribution. Regression-linear, polynomial. Distribution of the correlation coefficient, Partial and multiple correlation, Intraclass correlation,
Correlation ratio.
Standard errors and large sample test. Sampling distributions of sample mean, sample
variance, t, chi-square and F; tests of significance based on them, Small sample tests.
Non-parametric tests-Goodness of fit, sign, median, run, Wilcoxon, Mann-Whitney, WaldWolfowitz and Kolmogorov-Smirnov. Order statistics-minimum, maximum, range and
median. Concept of Asymptotic relative efficiency.
(iii) Numerical Analysis:
Finite differences of different orders: , E and D operators, factorial representation of a
polynomial, separation of symbols, sub-division of intervals, differences of zero.
Concept of interpolation and extrapolation: Newton Gregory's forward and backward
interpolation formulae for equal intervals, divided differences and their properties, Newton's
formula for divided difference, Lagrange’s formula for unequal intervals, central difference
formula due to Gauss, Sterling and Bessel, concept of error terms in interpolation formula.
Inverse interpolation: Different methods of inverse interpolation.
Numerical differentiation: Trapezoidal, Simpson’s one-third and three-eight rule and
Waddles rule.
Summation of Series: Whose general term (i) is the first difference of a function (ii) is in
geometric progression.
Numerical solutions of differential equations: Euler's Method, Milne’s Method, Picard’s
Method and Runge-Kutta Method.
(iv) Computer application and Data Processing:
Basics of Computer: Operations of a computer, Different units of a computer system like
central processing unit, memory unit, arithmetic and logical unit, input unit, output unit
etc., Hardware including different types of input, output and peripheral devices, Software,
system and application software, number systems, Operating systems, packages and
utilities, Low and High level languages, Compiler, Assembler, Memory – RAM, ROM, unit of
computer memory (bits, bytes etc.), Network – LAN, WAN, internet, intranet, basics of
computer security, virus, antivirus, firewall, spyware, malware etc.
Basics of Programming: Algorithm, Flowchart, Data, Information, Database, overview of
different programming languages, frontend and backend of a project, variables, control
structures, arrays and their usages, functions, modules, loops, conditional statements,
exceptions, debugging and related concepts.
STATISTICS- II (OBJECTIVE TYPE) (For ISS only)
(i) Linear Models:
Theory of linear estimation, Gauss-Markov linear models, estimable functions, error and
estimation space, normal equations and least square estimators, estimation of error
variance, estimation with correlated observations, properties of least square estimators,
generalized inverse of a matrix and solution of normal equations, variances and covariances
of least square estimators.
One way and two-way classifications, fixed, random and mixed effects models. Analysis of
variance (two-way classification only), multiple comparison tests due to Tukey, Scheffe and
Student-Newmann-Keul-Duncan.
(ii) Statistical Inference and Hypothesis Testing:
Characteristics of good estimator. Estimation methods of maximum likelihood, minimum
chi-square, moments and least squares. Optimal properties of maximum likelihood
estimators. Minimum variance unbiased estimators. Minimum variance bound estimators.
Cramer-Rao inequality. Bhattacharya bounds. Sufficient estimator. factorization theorem.
Complete statistics. Rao-Blackwell theorem. Confidence interval estimation. Optimum
confidence bounds. Resampling, Bootstrap and Jacknife.
Hypothesis testing: Simple and composite hypotheses. Two kinds of error. Critical region.
Different types of critical regions and similar regions. Power function. Most powerful and
uniformly most powerful tests. Neyman-Pearson fundamental lemma. Unbiased test.
Randomized test. Likelihood ratio test. Wald's SPRT, OC and ASN functions. Elements of
decision theory.
(iii) Official Statistics:
National and International official statistical system
Official Statistics: (a) Need, Uses, Users, Reliability, Relevance, Limitations, Transparency,
its visibility (b) Compilation, Collection, Processing, Analysis and Dissemination,
Agencies Involved, Methods
National Statistical Organization: Vision and Mission, NSSO and CSO; roles and
responsibilities; Important activities, Publications etc.
National Statistical Commission: Need, Constitution, its role, functions etc; Legal Acts/
Provisions/ Support for Official Statistics; Important Acts
Index Numbers: Different Types, Need, Data Collection Mechanism, Periodicity, Agencies
Involved, Uses
Sector Wise Statistics: Agriculture, Health, Education, Women and Child etc. Important
Surveys & Census, Indicators, Agencies and Usages etc.
National Accounts: Definition, Basic Concepts; issues; the Strategy, Collection of Data and
Release.
Population Census: Need, Data Collected, Periodicity, Methods of data collection,
dissemination, Agencies involved.
Misc: Socio Economic Indicators, Gender Awareness/Statistics, Important Surveys and
Censuses.
STATISTICS- III (DESCRIPTIVE TYPE) (For ISS only)
(i) Sampling Techniques:
Concept of population and sample, need for sampling, complete enumeration versus
sampling, basic concepts in sampling, sampling and Non-sampling error, Methodologies in
sample surveys (questionnaires, sampling design and methods followed in field
investigation) by NSSO.
Subjective or purposive sampling, probability sampling or random sampling, simple
random sampling with and without replacement, estimation of population mean,
population proportions and their standard errors. Stratified random sampling, proportional
and optimum allocation, comparison with simple random sampling for fixed sample size.
Covariance and Variance Function.
Ratio, product and regression methods of estimation, estimation of population mean,
evaluation of Bias and Variance to the first order of approximation, comparison with simple
random sampling.
Systematic sampling (when population size (N) is an integer multiple of sampling size (n)).
Estimation of population mean and standard error of this estimate, comparison with simple
random sampling.
Sampling with probability proportional to size (with and without replacement method), Des
Raj and Das estimators for n=2, Horvitz-Thomson’s estimator
Equal size cluster sampling: estimators of population mean and total and their standard
errors, comparison of cluster sampling with SRS in terms of intra-class correlation
coefficient.
Concept of multistage sampling and its application, two-stage sampling with equal number
of second stage units, estimation of population mean and total.Double sampling in ratio
and regression methods of estimation.
Concept of Interpenetrating sub-sampling.
(ii) Econometrics:
Nature of econometrics, the general linear model (GLM) and its extensions, ordinary least
squares (OLS) estimation and prediction, generalized least squares (GLS) estimation and
prediction, heteroscedastic disturbances, pure and mixed estimation.
Auto correlation, its consequences and tests. Theil BLUS procedure, estimation and
prediction, multi-collinearity problem, its implications and tools for handling the problem,
ridge regression.
Linear regression and stochastic regression, instrumental variable estimation, errors in
variables, autoregressive linear regression, lagged variables, distributed lag models,
estimation of lags by OLS method, Koyck’s geometric lag model.
Simultaneous linear equations model and its generalization, identification problem,
restrictions on structural parameters, rank and order conditions.
Estimation in simultaneous equations model, recursive systems, 2 SLS estimators, limited
information estimators, k-class estimators, 3 SLS estimator, full information maximum
likelihood method, prediction and simultaneous confidence intervals.
(iii) Applied Statistics:
Index Numbers: Price relatives and quantity or volume relatives, Link and chain relatives
composition of index numbers; Laspeyre's, Paasches’, Marshal Edgeworth and Fisher index
numbers; chain base index number, tests for index number, Construction of index
numbers of wholesale and consumer prices, Income distribution-Pareto and Engel curves,
Concentration curve, Methods of estimating national income, Inter-sectoral flows, Interindustry table, Role of CSO. Demand Analysis
Time Series Analysis: Economic time series, different components, illustration, additive and
multiplicative models, determination of trend, seasonal and cyclical fluctuations.
Time-series as discrete parameter stochastic process, auto covariance and autocorrelation
functions and their properties.
Exploratory time Series analysis, tests for trend and seasonality, exponential and moving
average smoothing. Holt and Winters smoothing, forecasting based on smoothing.
Detailed study of the stationary processes: (1) moving average (MA), (2) auto regressive (AR),
(3) ARMA and (4) AR integrated MA (ARIMA) models. Box-Jenkins models, choice of AR and
MA periods.
Discussion (without proof) of estimation of mean, auto covariance and autocorrelation
functions under large sample theory, estimation of ARIMA model parameters.
Spectral analysis of weakly stationary process, periodogram and correlogram analyses,
computations based on Fourier transform
STATISTICS-IV (DESCRIPTIVE TYPE) (For ISS only)
(Equal number of questions i.e. 50% weightage from all the subsections below
and
candidates have to choose any two subsections and answer)
(i) Operations Research and Reliability:
Definition and Scope of Operations Research: phases in Operation Research, models and
their solutions, decision-making under uncertainty and risk, use of different criteria,
sensitivity analysis.
Transportation and assignment problems. Bellman’s principle of optimality, general
formulation, computational methods and application of dynamic programming to LPP.
Decision-making in the face of competition, two-person games, pure and mixed strategies,
existence of solution and uniqueness of value in zero-sum games, finding solutions in 2x2,
2xm and mxn games.
Analytical structure of inventory problems, EOQ formula of Harris, its sensitivity analysis
and extensions allowing quantity discounts and shortages. Multi-item inventory subject to
constraints. Models with random demand, the static risk model. P and Q- systems with
constant and random lead times.
Queuing models – specification and effectiveness measures. Steady-state solutions of
M/M/1 and M/M/c models with associated distributions of queue-length and waiting
time. M/G/1 queue and Pollazcek-Khinchine result.
Sequencing and scheduling problems. 2-machine n-job and 3-machine n-job problems with
identical machine sequence for all jobs
Branch and Bound method for solving travelling salesman problem.
Replacement problems – Block and age replacement policies.
PERT and CPM – basic concepts. Probability of project completion.
Reliability concepts and measures, components and systems, coherent systems, reliability
of coherent systems.
Life-distributions, reliability function, hazard rate, common univariate life distributions –
exponential, weibull, gamma, etc. Bivariate exponential distributions. Estimation of
parameters and tests in these models.
Notions of aging – IFR, IFRA, NBU, DMRL and NBUE classes and their duals. Loss of
memory property of the exponential distribution.
Reliability estimation based on failure times in variously censored life-tests and in tests
with replacement of failed items. Stress-strength reliability and its estimation.
(ii) Demography and Vital Statistics:
Sources of demographic data, census, registration, ad-hoc surveys, Hospital records,
Demographic profiles of the Indian Census.
Complete life table and its main features, Uses of life table. Makehams and Gompertz
curves. National life tables. UN model life tables. Abridged life tables. Stable and stationary
populations.
Measurement of Fertility: Crude birth rate, General fertility rate, Age specific birth rate,
Total fertility rate, Gross reproduction rate, Net reproduction rate.
Measurement of Mortality: Crude death rate, Standardized death rates, Age-specific death
rates, Infant Mortality rate, Death rate by cause.
Internal migration and its measurement, migration models, concept of international
migration. Net migration. International and postcensal estimates. Projection method
including logistic curve fitting. Decennial population census in India.
(iii) Survival Analysis and Clinical Trial:
Concept of time, order and random censoring, likelihood in the distributions – exponential,
gamma, Weibull, lognormal, Pareto, Linear failure rate, inference for these distribution.
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Life tables, failure rate, mean residual life and their elementary classes and their
properties.
Estimation of survival function – actuarial estimator, Kaplan – Meier estimator, estimation
under the assumption of IFR/DFR, tests of exponentiality against non-parametric classes,
total time on test.
Two sample problem – Gehan test, log rank test.
Semi-parametric regression for failure rate – Cox’s proportional hazards model with one
and several covariates, rank test for the regression coefficient.
Competing risk model, parametric and non-parametric inference for this model.
Introduction to clinical trials: the need and ethics of clinical trials, bias and random error
in clinical studies, conduct of clinical trials, overview of Phase I – IV trials, multicenter
trials.
Data management: data definitions, case report forms, database design, data collection
systems for good clinical practice.
Design of clinical trials: parallel vs. cross-over designs, cross-sectional vs. longitudinal
designs, review of factorial designs, objectives and endpoints of clinical trials, design of
Phase I trials, design of single-stage and multi-stage Phase II trials, design and monitoring
of phase III trials with sequential stopping,
Reporting and analysis: analysis of categorical outcomes from Phase I – III trials, analysis
of survival data from clinical trials.
(iv) Quality Control:
Statistical process and product control: Quality of a product, need for quality control, basic
concept of process control, process capability and product control, general theory of control
charts, causes of variation in quality, control limits, sub grouping summary of out of
control criteria, charts for attributes p chart, np chart, c-chart, V chart, charts for
variables: R, (
X ,R), (
X ,σ) charts.
Basic concepts of process monitoring and control; process capability and process
optimization. General theory and review of control charts for attribute and variable data;
O.C. and A.R.L. of control charts; control by gauging; moving average and exponentially
weighted moving average charts; Cu-Sum charts using V-masks and decision intervals;
Economic design of X-bar chart.
Acceptance sampling plans for attributes inspection; single and double sampling plans and
their properties; plans for inspection by variables for one-sided and two sided specification.
(v) Multivariate Analysis:
Multivariate normal distribution and its properties. Random sampling from multivariate
normal distribution. Maximum likelihood estimators of parameters, distribution of sample
mean vector.
Wishart matrix – its distribution and properties, distribution of sample generalized
variance, null and non-null distribution of multiple correlation coefficients.
Hotelling’s T2 and its sampling distribution, application in test on mean vector for one and
more multivariate normal population and also on equality of components of a mean vector
in multivariate normal population.
Classification problem: Standards of good classification, procedure of classification based
on multivariate normal distributions.
Principal components, dimension reduction, canonical variates and canonical correlation —
definition, use, estimation and computation.
(vi) Design and Analysis of Experiments:
Analysis of variance for one way and two way classifications, Need for design of
experiments, basic principle of experimental design (randomization, replication and local
control), complete analysis and layout of completely randomized design, randomized block
design and Latin square design, Missing plot technique. Split Plot Design and Strip Plot
Design.
Factorial experiments and confounding in 2n and 3n experiments. Analysis of covariance.
Analysis of non-orthogonal data. Analysis of missing data.
(vii) Computing with C and R :
Basics of C: Components of C language, structure of a C program, Data type, basic data
types, Enumerated data types, Derived data types, variable declaration, Local, Global,
Parametric variables, Assignment of Variables, Numeric, Character, Real and String
constants, Arithmetic, Relation and Logical operators, Assignment operators, Increment
and decrement operators, conditional operators, Bitwise operators, Type modifiers and
expressions, writing and interpreting expressions, using expressions in statements. Basic
input/output.
Control statements: conditional statements, if - else, nesting of if - else, else if ladder,
switch statements, loops in c, for, while, do - while loops, break, continue, exit ( ), goto and
label declarations, One dimensional two dimensional and multidimensional arrays. Storage
classes: Automatic variables, External variables, Static variables, Scope and lifetime of
declarations.
Functions: classification of functions, functions definition and declaration, assessing a
function, return statement, parameter passing in functions. Pointers (concept only).
Structure: Definition and declaration; structure (initialization) comparison of structure
variable; Array of structures : array within structures, structures within structures,
passing structures to functions; Unions accessing a union member, union of structure,
initialization of a union variable, uses of union. Introduction to linked list, linear linked list,
insertion of a node in list, removal of a node from list.
Files in C: Defining and opening a file, input – output operation on a file, creating a file,
reading a file.
Statistics Methods and techniques in R
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