Description

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.

Textbooks

A self-contained lecture note is the main source of reference. Complementary textbooks include

• (Major) Casella, G. and Berger, R. L. (2002). Statistical Inference. Duxbury Press.
• (Minor) Wasserman, L. (2013). All of statistics: a concise course in statistical inference. Springer.

Learning outcomes

Upon finishing the course, students are expected to

1. apply basic statistics limit theorems and probability inequalities;
2. perform data reduction through various kind of statistical principles;
3. derive point estimation, interval estimation and testing procedures, and study their properties;
4. analyze and evaluate statistical procedures by different criteria, and understand the interpretations of those criteria.

Assessment and Grading

The final score (out of 100) is given by {40a+20max(m,f)+40f}/100, where

• a (out of 100) is the average score of approximately eight assignments with the lowest two scores dropped;
• m (out of 100) is the score of mid-term exam; and
• f (out of 100) is the score of final exam.