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Paper II of the Indian Statistical Service written examination is Statistics-Ii, and this page takes its syllabus one line at a time. Each line is reproduced as it is prescribed, then pointed at the page on this site that teaches it, with the depth stated rather than implied.

Statistics-II (Objective) — 200 marks, 2 hrs.

Examination Notice No. 07/2026-IES/ISS, dated 11.02.2026 — Appendix-I, Scheme of Examination, and Section-II, Standard and Syllabi

Section (i) — Linear Models

6 syllabus lines: 5 taught in depth, 1 at exam level, 0 not here yet.

Syllabus line, as prescribedWhere it is taught hereDepth
Theory of linear estimation; Gauss–Markov linear models; estimable functions; error and estimation spaceLinear Algebra & Linear Models Unit 4 — Linear Models: Estimability, Gauss-Markov and Aitkendeep
Normal equations and least square estimators; estimation of error variance; estimation with correlated observations; properties of least square estimatorsLinear Algebra & Linear Models Unit 4 — Linear Models: Estimability, Gauss-Markov and Aitkendeep
Generalized inverse of a matrix and solution of normal equations; variances and covariances of least square estimatorsLinear Algebra & Linear Models Unit 1 — Vector Spaces, Gram-Schmidt and Generalized Inverses
Linear Algebra & Linear Models Unit 4 — Linear Models: Estimability, Gauss-Markov and Aitken		deep
One-way and two-way classifications; fixed, random and mixed effects modelsDesign and Analysis of Experiments Unit 1 — Two-Way ANOVA with Several Observations per Cell, Multiple Comparisons and ANCOVA
UGC NET Unit III — Sampling Methods & Design of Experiments		brief
Analysis of variance, two-way classification onlyDesign & Analysis of Experiments Unit 1 — Analysis of Variance (ANOVA)deep
Multiple comparison tests due to Tukey, Scheffé and Student–Newman–Keuls–DuncanDesign and Analysis of Experiments Unit 1 — Two-Way ANOVA with Several Observations per Cell, Multiple Comparisons and ANCOVAdeep

Section (ii) — Statistical Inference and Hypothesis Testing

12 syllabus lines: 12 taught in depth, 0 at exam level, 0 not here yet.

Syllabus line, as prescribedWhere it is taught hereDepth
Characteristics of a good estimator; estimation by maximum likelihood, minimum chi-square, moments and least squares; optimal properties of maximum likelihood estimatorsEstimation Theory Unit 2 — Completeness, Lehmann-Scheffé, CAN and BAN, Jackknife and Bootstrapdeep
Minimum variance unbiased estimators; minimum variance bound estimators; Cramér–Rao inequality; Bhattacharya boundsEstimation Theory Unit 1 — UMVU Estimation, Cramér-Rao and Rao-Blackwelldeep
Sufficient estimator; factorization theorem; complete statistics; Rao–Blackwell theoremEstimation Theory Unit 1 — UMVU Estimation, Cramér-Rao and Rao-Blackwelldeep
Confidence interval estimation; optimum confidence boundsEstimation Theory Unit 3 — U-Statistics, Interval Estimation and Tolerance Limitsdeep
Resampling, bootstrap and jackknifeEstimation Theory Unit 2 — Completeness, Lehmann-Scheffé, CAN and BAN, Jackknife and Bootstrapdeep
Hypothesis testing: simple and composite hypotheses; two kinds of error; critical region; power functionInferential Statistics Unit 2 — Testing of Hypothesisdeep
Different types of critical regions and similar regionsTesting of Hypotheses Unit 2 — UMP Tests, Monotone Likelihood Ratio and Similar Regionsdeep
Most powerful and uniformly most powerful tests; Neyman–Pearson fundamental lemmaTesting of Hypotheses Unit 1 — Randomized Tests and the Complete Neyman–Pearson Lemmadeep
Unbiased test; randomized testTesting of Hypotheses Unit 2 — UMP Tests, Monotone Likelihood Ratio and Similar Regionsdeep
Likelihood ratio testTesting of Hypotheses Unit 3 — The Likelihood Ratio Test, Wald and Rao Scoredeep
Wald's SPRT, OC and ASN functionsTesting of Hypotheses Unit 4 — Sequential Analysis and Decision Theorydeep
Elements of decision theoryEstimation Theory Unit 4 — Decision Theory, Bayes and Minimax, and Density Estimationdeep

Section (iii) — Official Statistics

9 syllabus lines: 1 taught in depth, 4 at exam level, 4 not here yet.

Syllabus line, as prescribedWhere it is taught hereDepth
Official statistics: need, uses, users, reliability, relevance, limitations, transparency, visibilitynothing on this site teaches itnot here
Compilation, collection, processing, analysis and dissemination; agencies involved; methodsnothing on this site teaches itnot here
National Statistical Organization: vision and mission; NSSO and CSO, roles and responsibilities, activities and publicationsUGC NET Unit X — Indian Statistical System & Research Methodologybrief
National Statistical Commission: need, constitution, role and functions; legal acts and provisions for official statisticsUGC NET Unit X — Indian Statistical System & Research Methodologybrief
Index numbers: types, need, data collection mechanism, periodicity, agencies involved, usesApplied Statistics Unit 3 — Index Numbersdeep
Sector-wise statistics — agriculture, health, education, women and child; important surveys and censuses, indicators, agenciesnothing on this site teaches itnot here
National accounts: definition, basic concepts, issues, strategy, collection of data and releaseNational Income and the National Accounts — Economics (Unit 2)brief
Population census: need, data collected, periodicity, methods of collection, dissemination, agenciesApplied Statistics Unit 4 — Vital Statisticsbrief
Socio-economic indicators; gender awareness and statisticsnothing on this site teaches itnot here

What this paper still needs

Not covered yet — 4 lines in Paper II. Read these from a standard text; this site does not yet teach them.

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