A tentative schedule for Inference I:
Week 1: Motivation and definitions
Week 2: Sufficiency
Week 3: Exponential families
Week 4: Exponential families and ML
Week 5: Bias& variance, unbiased estimators, UMVUE
Week 6: Fisher-information, Cramer-Rao lower bound
Week 7: Bayesian Inference, Conjugate prior
Week 8: Empirical Bayes, Hierarchical Bayes.
Week 9: Admissibility, James-Stein estimator, admissible James-Stein estimators
Week 10: Bayes computations; numeric integration, MC, and MCMC.
Week 11: Minimaxity and connection to Bayesian estimation
Week 12: Analytic functions and minimaxity for normal mean
Week 13: Kneser-Kuhn Theorem and minimax theorem for convex loss
Week 14: Vector-valued normal mean problem and admissibility
A tentative schedule for Inference II:
Week 1: Stochastic convergence (Review)
Week 2: Asymptotic analysis of MLE
Week 3: Asymptotic analysis of MLE
Week 4: M-estimators
Week 5: Basics of hypothesis testing, Neyman-Pearson lemma
Week 6: Uniformly most powerful tests
Week 7: Unbiased tests (UMPU tests)
Week 8: Invariant tests
Week 9: Multiple testing
Week 10: Multiple testing
Week 11: Asymptotic analysis of tests (Basic tools)
Week 12: Quadratic mean differentiability
Week 13: Large sample optimality
Week 14: Likelihood ratio tests