Cheung: 01-07

P8109 Course description

This course is designed for first year Master's and DrPH students in biostatistics. The primary objective is to present the mathematical structure of statistical inference procedures. In particular, the class will study estimation theory, confidence sets, testing, and prediction in common parametric models. Selected topics on estimation and testing procedures will also be discussed if time permits (see a partial list below). The materials will be presented at a rigorous but not advanced level. Students should have a solid calculus background, some knowledge of linear algebra, and adequate familiarity with basic probability theory (P8104 or equivalent).

Course Outline:

1. Probability theory (quick review): Statistical models; random variables; distribution theory; limit theorems. (Chapters 1-5)
2. Estimation: Method of moments; maximum likelihood estimation; Fisher information; confidence intervals; sufficient statistics; empirical distribution function; nonparametric procedures. (Chapters 6, 7, 9)
3. Hypothesis testing: Neyman-Pearson Lemma; likelihood ratio test; Wald's test; permutation test; test inversion; multiple testing. (Chapter 10)
4. Special topics: Bayes estimation; decision theory; bootstrap; least squares estimation; empirical bayes. (Chapters 8, 11, 12)