Indian Statistical Service Exam
1. Linear Models: Theory of linear estimation. Gauss-Markoff
setup. Least square estimators. Use of ginverse. analysis of one-way and two way
classified data-fixed, mixed and random effect models. Tests for regression
2. Estimation: 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. factorisation theorem. Complete
statistics. Rao-Blackwell theorem. Confidence interval estimation. Optimum
confidence bounds. Resampling, Bootstrap and Jacknife.
3. Hypotheses testing and Statistical Quality Control: (a) Hypothesis
testing: Simple and composite hypothesis. Two kinds of error. Critical region.
Different types of critical regions and similar regions. Power function.
Mostpowerful and uniformly most powerful tests. Neyman-Pearson fundamental
lemma. Unbiased test. Randomised test. Likelihood ratio test. Wald’s SPRT, OC
and ASN functions. Elements of decision and game theory. b) Statistical Quality
Control: Control Charts for variable and attributes. Acceptance Sampling by
attributes-Single, double, multiple and sequential Sampling plans; Concepts of
AOQL and ATI; Acceptance Sampling by variables-use of Dodge-Romig and other
4. Multivariate Analysis: Multivariate normal distribution. Estimation
of mean Vector and covariance matrix. Distribution of Hotelling’s T2-statistic,
Mahalanobis’s D2-statistic, and their use in testing. Partial and multiple
correlation coefficients in samples from a multivariate normal population.
Wishart’s distribution, its reproductive and other properties. Wilk’s criterion.
Discriminant function. Principal components. Canonical variates and