Point Estimation (Parametric): unbiasedness, consistency, efficiency, method of moments and maximum likelihood, lower bounds for the variance of an estimator, Frechet-Rao-Cramer, Bhattacharya, Chapman Robbins-Kiefer inequalities. Sufficiency, minimal sufficiency, Factorization Theorem, Rao-Blackwell Theorem, completeness, Lehmann-Scheffe Theorem, UMVUE, Basu’s Theorem, invariance, best equivariant estimators
Testing of Hypotheses: Tests of hypotheses, simple and composite hypotheses, types of error, Neyman-Pearson Lemma, families with a monotone likelihood ratio, UMP, UMP unbiased, and UMP invariant tests. Likelihood ratio tests - applications to one sample and two sample problems, Chi-square tests. Wald’s sequential probability ratio test.
Interval estimation: methods for finding confidence intervals, shortest length confidence intervals.

The objective of this course is to learn various techniques related to statistical inference.

On completion of this course, the students would be able to apply statistical inferential techniques to estimate some unknown parameters and characteristics of a statistical model. Further, they would be able to conclude the correct statement about the values of the unknown parameters.

G. Casella and R. L. Berger, Statistical inference, Wadsworth cengage learning

V.K. Rohatgi & A.K. Md. E. Saleh., An Introduction to Probability and Statistics, Wiley

B K Kale, A First Course on Parametric Inference, Alpha Science International Ltd

R. E. Walpole, R. H. Myers, S. L. Myers and K. Ye, Probability and Statistics for Engineers and Scientists, Pearson Education Inc.