Instructor: José Luis Montiel Olea
Class schedule:
Time | Place |
---|---|
Wednesday 10.00am - 11.15am | 403 International Affairs Building |
Wednesday 1.10pm - 2.25pm | 227 Seeley W. Mudd Building |
The syllabus is available here
Wednesday 6:00pm-7:00pm. Please register here
Class | Topic | Slides/Notes | References/Suggested reading |
---|---|---|---|
Probability Theory | |||
1 | Probability spaces, real-valued random variables | Slides 1-2 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 | Slides 3-4 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. Identification, statistical sufficiency. The Normal Linear Regression Model | Lectures 5-6 | Class Notes, pp. 1-4 |
6 | Elements of a finite-sample statistical decision problem: loss function, risk function, decision rules. Bayes and minimax decision rules: a primer | Pset 3 | Class Notes, pp. 5-7 |
Point Estimation | |||
7 | Maximum Likelihood and Bayesian estimators for the Normal 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 | 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 5 | Class Notes, pp. 7-9 |