M567 - Statistical Inference II

Course No: 
M481 or equivalent course

General decision problem, loss and risk function, minimax estimation, minimaxity and admissibility in exponential family (5 hrs)

Introduction to Bayesian estimation, Bayes rule as average risk optimality, prior and posterior, conjugate families, generalized Bayes rules (8 hrs)

Bayesian intervals and construction of credible sets, Bayesian hypothesis testing (8 hrs)

Empirical and nonparametric empirical Bayes analysis, admissibility of Bayes and generalized Bayes rules, discussion on Bayes versus non-Bayes approaches (7 hrs)

Large sample theory: review of modes of convergences, Slutsky’s theorem, Berry-Essen bound, delta method, CLT for iid and non iid cases, multivariate extensions (10 hrs)

Asymptotic level  tests, asymptotic equivalence, comparison of tests: relative efficiency, asymptotic comparison of estimators, efficient estimators and tests, local asymptotic optimality (11 hrs)


Bootstrap sampling: estimation and testing (5 hrs)

Reference Books: 
  1. Lehmann, E.L. and Romano, J. P. (2005), “Testing Statistical Hypotheses”, 3rd edition, Springer.
  2. Lehmann, E.L. (1999), “Elements of Large-Sample Theory”, Springer-Verlag.
  3. James O Berger (1985), “Statistical Decision Theory and Bayesian Analysis”, 2nd Edition, New York: Springer.
  4. Lehmann, E.L. and Casella, G.(1998), “Theory of Point Estimation”, 2nd edition, New York: Springer 

Contact us

School of Mathematical Sciences

NISERPO- Bhimpur-PadanpurVia- Jatni, District- Khurda, Odisha, India, PIN- 752050

Tel: +91-674-249-4081

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