Course Description

This course focuses on drawing large sample inferences about "parameters" in statistical models. We develop asymptotic theory for maximum likelihood estimation, M-estimation, and generalized method of moment (GMM) estimation. Formal techniques for constructing estimators in semi-parametric models will be discussed. Particular attention will be paid to models for longitudinal and survival data. Guest lecturers will discuss special topics (e.g., targeted maximum likelihood, hypothesis testing, empirical likelihood). The course will involve rigorous mathematical arguments so that familiarity with concepts in advanced calculus, real analysis, and measure theory will be required.

Intended Audience

The course is designed for Biostatistics Ph.D. students in their 2nd year or beyond. Exceptions made with permission of the instructor.

Prerequisites

Introduction to Probability Theory I-II (550.620-1), Introduction to Statistical Theory I-II (140.673-4), Real Analysis.

Recommended Textbooks

__Theory of Point Estimation__, by E.L. Lehmann and G. Casella, Springer__A Course in Large Large Sample Theory__, by T.S. Ferguson, Chapman-Hall__Elements of Large-Sample Theory__, by E.L. Lehmann, Springer__Approximation Theorems of Mathematical Statistics__, by R Serfling, Wiley__Asymptotic Statistics__, by A.W. van der Vaart, Cambridge__Large Sample Estimation and Hypothesis Testing__, by W.K. Newey and D. McFadden, Handbook of Econometrics__Theoretical Statistics, by D. Cox and D. Hinkley__, Chapman and Hall__Principles of Mathematical Analysis__, by W. Rudin, McGraw Hill__Counting Processes and Survival Analysis__, by T. Fleming and D. Harrington, Wiley__Probability and Measure__, by P. Billingsley, Wiley__Real Analysis and Probability__, by R. Ash, Academic Press__Optimization by Vector Space Methods__, by D. Luenberger, Wiley

Lecture Notes

- Chapter 1: Brief Introduction
- Chapter 2: Analysis and Asymptotics – Review
- Chapter 3: Asymptotic Theory of Estimation
- Chapter 4.1: Asymptotic Properties of the MLE – Part 1
- Chapter 4.2: Asymptotic Properties of the MLE – Part 2
- Chapter 4.3: Asymptotic Properties of the MLE – Part 3
- Chapter 5: Generalized Method of Moments
- Chapter 6: Hilbert Space for Random Vectors
- Chapter 7: Influence Functions
- Chapter 8: Semiparametric Models
- Chapter 9: Stochastic Processes/Survival Analysis

Homeworks