Statistics - II paper of Indian Statistical Services is of objective type with 80 questions and 200 marks. The duration of the paper is 2 hours. The syllabus has three sections - Linear Models, Statistical Inference & Hypothesis Testing, and Official Statistics.

### 1. 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.

### 2. 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.

### 3. 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.