This half-course constitutes the first six weeks in a first-year graduate econometric sequence. After reviewing basic probability concepts, it provides the basic tools for large-sample analysis in econometrics, and sets up a decision-theoretic framework that allows us to think about estimation and testing in a rigorous way. You will use these tools throughout the remainder of the first year and beyond. We also cover some foundational results that are important in their own right, such as the complete class theorem.
For Princeton students, homework and solutions to it will be posted on Canvas. Official course description is at the Registrar's website.
This repository provides detailed lecture notes with references. They aim to be self-contained, so they can also serve as a reference in your later graduate work. As such, a textbook is not needed to survive this course. If your course goal is more ambitious than that, it is useful to buy one a the three textbooks listed in the syllabus so that you can get a different perspective on the material covered.
- Probability review: probability spaces, random variables, transformations of random variables, quantiles, expectations, independence, covariance, the multivariate normal distribution Notes
- Convergence, law of large numbers, central limit theorem, delta method Notes
- Statistical decision theory, game theory, and expected utility. Admissibility, unbiasedness, minimax risk, asymptotic properties of estimators Notes
- Sufficient statistics, factorization theorem, Rao-Blackwell theorem Notes
- Maximum likelihood, Fisher information, the information (Cramér-Rao) bound, and the method of moments. Notes
- Large-sample properties of maximum likelihood estimators. Maximum likelihood is asymptotically normal. It is also asymptotically minimax. Notes
- Bayesian concepts. Complete class theorem. A good frequentist agrees with at least one Bayesian in finite samples; no frequentist is allowed to make fun of any non-dogmatic Bayesian. Notes
- Testing concepts. Notes
- Testing in small samples. Neyman-Pearson lemma. Unbiased tests. Notes
- Testing in large samples. Wald, Score and likelihood ratio tests are asymptotically chi-squared. They are also asymptotically optimal. Notes
- Confidence sets. Bernstein-von Mises theorem. All good frequentists and non-dogmatic Bayesians agree in large samples. Notes
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