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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

courses-introeconometrics-ph.d's Introduction

Fall 2019

Course Info

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

Syllabus

The syllabus is available here

Office Hours

Wednesday 6:00pm-7:00pm. Please register here

Material

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

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