MATH 4261: Mathematical Statistics I
Georgia Institute of Technology, Fall 2026
This is the first of a two-part course in mathematical statistics. After reviewing probability, we study sampling distributions, the delta method, parametric estimation, maximum likelihood and Bayesian methods, confidence intervals, and hypothesis testing.
References
- Morris H. DeGroot and Mark J. Schervish, Probability and Statistics.
- Robert V. Hogg, Joseph W. McKean, and Allen T. Craig, Introduction to Mathematical Statistics.
- John A. Rice, Mathematical Statistics and Data Analysis.
- Larry Wasserman, All of Statistics.
I gratefully acknowledge Zhou Fan, Cheng Mao, and Yihong Wu for sharing their teaching materials, which formed the basis for this course.
Lecture
| Date | Lecture |
|---|---|
| Aug 24 | Lecture 1: Course introduction, Survey Sampling |
| Aug 26 | Lecture 2: Probability Review I |
| Aug 31 | Lecture 3: Probability Review II, Multivariate Normal |
| Sep 2 | Lecture 4: Conditioning and Best Estimates |
| Sep 9 | Lecture 5: Sampling distributions, MGFs |
| Sep 14 | Lecture 6: LLN and CLT |
| Sep 16 | Lecture 7: Order statistics and quantiles |
| Sep 21 | Lecture 8: Quantile estimation II, and parameter estimation |
| Sep 23 | Lecture 9: Method of moments |
| Sep 28 | Lecture 10: Review 1 |
| Oct 7 | Lecture 11: Maximum likelihood estimation |
| Oct 12 | Lecture 12: Delta method |
| Oct 14 | Lecture 13: Properties of MLE |
| Oct 19 | Lecture 14: Fisher information and Cramér-Rao lower bound |
| Oct 21 | Lecture 15: Bayesian inference I: conjugacy |
| Oct 26 | Lecture 16: Bayesian inference II: credible sets |
| Oct 28 | Lecture 17: Parameter estimation under model misspecification |
| Nov 2 | Lecture 18: Review 2 |
| Nov 9 | Lecture 19: Joint distributions of estimators; chi-square and t distributions |
| Nov 11 | Lecture 20: Confidence intervals and pivotal quantities |
| Nov 16 | Lecture 21: Uncertainty quantification using the bootstrap |
| Nov 18 | Lecture 22: Hypotheses, errors, test statistics, and p-values |
| Nov 23 | Lecture 23: Likelihood-ratio, Z, and t tests |
| Nov 30 | Lecture 24: Power, Neyman-Pearson lemma |
| Dec 2 | Lecture 25: Goodness-of-fit tests, GLRT |
| Dec 7 | Lecture 26: Final review |