Stat 300A : SyllabusHere is a rough syllabus. As the class proceeds, I will add dates and some more details. (Dates are approximate.) Sep 24, 26
Statistical model and statistical estimators. Risk function. Minimax and Bayes optimality criteria. Sufficient statistics and the Neyman-Fisher criterion. Rao-Blackwell theorem. Exponential families. Oct 1, 3
Bayes optimality. Existence and characterization of Bayes optimal estimators. Examples: linear regression with Gaussian priors, binomial with Beta priors. Empirical Bayes methods. Connection with admissibility. Oct 8, 10, 15
Minimax optimality. The minimax theorem. Bayes lower bound and sufficient condition for minimax optimality. Examples: binomial mean; bounded normal mean. Optimality of least squares for bowl-shaped losses. The effect of invariance. Admissibility and the James-Stein estimator. Oct 17, 22, 24, 19
Approximate minimax. Minimax risk for the Gaussian location model over ellipsoids and Pinsker's theorem. Information theory: f-divergences and inequalities. Information theoretic lower bounds on the minimax risk: Fano's and Le Cam's methods. Application to sparse high-dimensional regression. Oct 31, Nov 5, 7
Revisiting sufficient statistics. Minimal and complete sufficient statistics. Unbiased estimation. UMVU estimators. Cram'er-Rao lower bound. Nov, 12, 14, 26, 27
Hypothesis testing. Neyman-Pearson's lemma. Monotone likelihood ratio families. UMP tests. Homeworks will be assigned every Wednesday, the first time on September 25, and due the following Wednesday (a total of 9 homeworks will be assigned). They can be submitted in class or in the homework box in Sequoia. An in-class midterm will be given on Friday, October 26, 3:30pm-6:30pm in room 380-380Y. You are allowed to bring and consult any of the textbooks (TPE, TSH), a printed copy of the lecture notes (or your own course notes), as well as the homeworks or homework solutions, but no other sources. |