yu45020 / Courses-IntroEconometrics-Ph.D

This course provides a graduate level introduction to probability and statistics. The course was designed for economists starting their doctoral education. Edits, comments, and suggestions are welcome.

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Statistics

Fall 2021

Course Info

Instructor: José Luis Montiel Olea

Class schedule:

Time Place
Monday 10am - 11.15am 303 Hamilton Hall
Monday 1pm - 2.25am 520 Mathematics Building

Syllabus

The syllabus is available here

Office Hours

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.

Material

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

About

This course provides a graduate level introduction to probability and statistics. The course was designed for economists starting their doctoral education. Edits, comments, and suggestions are welcome.

License:BSD 3-Clause "New" or "Revised" License