この講義では,次のようなかなり高度な数理統計学の教科書の内容を解説する。E.L. Lehmann and G. Casella "Theory of Point Estimation" (Second Edition, 1998, Springer), E.L. Lehmann and J.P. Romano "Testing Statistical Hypotheses" (Third Edition, 2010, Springer), (4) ベイズ推定(経験ベイズ,階層ベイズ,リスクの比較など)(5) ミニマックス性と許容性(ミニマックス推定,許容性,縮小推定,スタイン現象,完全類)(6) 漸近最適性 (II) 仮説検定の理論 (1) 一様最強力検定(Neyman-Pearson 補題とその拡張など)(2)不偏検定(一様最強力不偏検定の構成など)(3)不変検定
(This lecture is implemented in Japanese. It provides advanced level of mathematical statistics using the following high level of text books: E.L. Lehmann and G. Casella "Theory of Point Estimation" (Second Edition, 1998, Springer), and E.L. Lehmann and J.P. Romano "Testing Statistical Hypotheses" (Third Edition, 2010, Springer). (4) Bayes estimation (empirical Bayes, hierarchical Bayes, risk comparison) (5) minimaxity and admissibility (shrinkage estimator, Stein problem) (6) asymptotic optimality, (II) Hypotheses testing (1) Uniform most pw ***** test (Neyman-Pearson's lemma) (2) unbiased test (3) invariant test)