Probability and StatisticsGames and statistical games, statistical decision problem, decision function, risk function, prior and posterior distribution, Bayes risk, and Bayes rules, least favorable prior,
minimaxity, admissibility and complete classes, admissibility of Bayes rules, existence of minimal complete class and Bayes rules, the supporting and separating hyperplane theorems, essential completeness of the class of nonrandomized rules, minimax, and complete class theorems solving for minimax rules, essential completeness of class of rules based on sufficient statistics,
continuity of risk functions, invariant decision problems, admissible and minimax invariant decision rules.

The objective of this course is to know various important concepts of statistical decision theory and its implementation to practical problems.

After completing this course, students will be able to judge the best estimator in a class of estimators. They will know how to use the concepts of statistical decision theory in many practical problems.

John Pratt, Howard Raiffa, Robert Schlaifer, Introduction to Statistical Decision Theory, The MIT Press

J. O. Berger, Statistical Decision Theory and Bayesian Analysis, Springer

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

G. Casella & R.L. Berger., Statistical Inference, Wadsworth Cengage Learning