Instructor: José Luis Montiel Olea
Class schedule:
| Time | Place |
|---|---|
| Monday 10am - 11.15am | 303 Hamilton Hall |
| Monday 1pm - 2.25am | 520 Mathematics Building |
The syllabus is available here
I will have 1 hour of office hours every week. In the past I have asked the students to register in this link. We will decide together what time works best for everyone.
| Class | Topic | Slides/Notes | References/Suggested reading |
|---|---|---|---|
| Probability Theory | |||
| 1 | Probability spaces, real-valued random variables | Lectures 1-2 | Class Notes, pp. 1-5 |
| 2 | Cumulative distribution functions, moments, moment generating functions | Pset 1 | Class Notes, pp. 5-9 |
| 3 | Vector-valued random variables, multivariate distributions/densities/expectations, moment generating functions of random vectors | Lectures 3-4 | Class Notes, pp. 1-6 |
| 4 | Independence, conditional probability, conditional expectation | Pset 2 | Class Notes, pp. 7-15 |
| Mathematical Statistics | |||
| 5 | Statistical models and statistical decision problems | Lectures 5-6 | Class Notes, pp. 1-4 |
| 6 | Bayes and minimax decision rules: a primer | Pset 3 | Class Notes, pp. 5-7 |
| Point Estimation | |||
| 7 | Maximum Likelihood and Bayesian estimators for the Linear Regression model | Lectures 7-8 | Class Notes, pp. 1-7 |
| 8 | Bias, Mean-squared error, some optimality results concerning OLS, Cramer-Rao bound, James-Stein/Empirical Bayes estimators | Pset 4 | Class Notes, pp. 7-11 |
| Hypothesis Testing | |||
| 9 | Null and alternative hypotheses, Type I/II error | Lectures 9-10 | Class Notes, pp. 1-6 |
| 10 | Neyman-Pearson lemma, Score/LR/Wald tests | Pset 5 | Class Notes, pp. 6-13 |
| Confidence Sets | |||
| 11 | Coverage of a confidence set, Expected Length of a confidence interval, Higher posterior density regions. Constructing confidence sets via test inversion. | Lectures 11-12 | Class Notes, pp. 1-6 |
| 12 | Parametric bootstrap and credible sets | Pset 6 | Class Notes, pp. 7-9 |