This course provides an introduction to statistical inference. Topics include statistical models, sampling distributions, asymptotic distributions, sufficiency, maximum likelihood estimation, Bayesian estimation, Rao-Blackwell theorem, Cramér-Rao theorem and the best unbiased estimator, Neyman-Pearson lemma, uniformly most powerful test and general likelihood ratio test.
Upon finishing the course, students are expected to
- apply basic statistics limit theorems and probability inequalities;
- perform data reduction through various kind of statistical principles;
- derive point estimation, interval estimation and testing procedures, and study their properties;
- analyze and evaluate statistical procedures by different criteria, and understand the interpretations of those criteria.