Mathematical Statistics

Syllabus

• Statistical experiments; empirical distributions and the Glivenko–Cantelli theorem.
• Sufficiency, completeness, Fisher information, and the foundations of point estimation.
• Properties of estimators: unbiasedness, admissibility, minimaxity, efficiency, and consistency.
• Blackwellization, information bounds, empirical estimators, the method of moments, maximum likelihood estimation, and Bayesian estimation.
• Hypothesis testing and statistical tests; the Neyman–Pearson lemma.
• Classical parametric tests, chi-squared tests, and classical nonparametric tests.
• Multivariate normal distributions and parameter estimation.
• Estimation and hypothesis testing in linear models.
• Confidence sets and confidence intervals.