## S722: Advanced Statistical Theory Il

### Class Description

A continuation of S-721. A mathematical introduction to major areas of statistical theory and practice including multinomial models, canonical linear models, exponential families, asymptotic theory. Methods of point estimation, hypothesis testing and confidence intervals. Connections between frequentist and Bayesian approaches.

### Class Information

**School/Department: **Statistics

**Semester(s): **Spring

**Class time: **
Monday, Wednesday

**Capacity: ** Enrollment for Spring 2012 was 6 students.

### Contact Information

**Instructor: **Chunfeng Huang - huang48@indiana.edu

**Other Contact(s): ** Chunfeng Huang - huang48@indiana.edu

### Other Details

**Sequence: ** This course is part of the sequence Stat-S 721-722 Advanced Statistical Analysis Theory I-II.

**Prerequisites: ** Stat S-721. Advanced Statistical Analysis Theory I.

**Algebra Required?: ** Some knowledge of matrix algebra if class is extended to cover methods on linear models. There are proofs along homeworks, class examples and tests.

**Calculus Required?: ** A good knowledge of integration and differentiation is needed. Some notions of Real Analysis like formal definitions of limits and continuity are useful.

**Day(s) per week offered: ** It was taught TR in 75-minute class meetings. It can be taught in the MWF format. No computer lab.

**Recommended follow-up classes: ** S-721-722 define the first year core theory courses in statistical inferences for the Ph.D program in Statistics. After this class, students are prepared for other S-700+ courses.

**Substantive Orientation: ** This course is designed for the Ph.D students in Statistics. In Spring 2012, the course was also attended by a Ph.D student in Mathematics and a Ph.D. student in the School of Informatics.

**Statistical Orientation: ** Statistical inference theory and methods

**Books used: ** For Spring 2012 the textbook was Casella, G. and Berger, R. L. (2001) Statistical Inference, 2nd Edition. Duxbury Press. Selected material from Chapters 5-10. Stat-721 used the same textbook with material from Chapters 1-5. Stat-721 was taught by Professor Rocha. An excellent supplemental text is Severini, T. (2001). Elements of Distribution Theory. Cambridge Series in Statistical and Probabilistic Mathematics.

**Applied/Theoretical: ** This is a theoretical course. Some data examples are considered.

**Software Used: **
R

**How the software is used: ** Numerical illustrations of optimization, maximum likelihood estimation.

**Problem Sets: ** Yes. In the range of 6-8 homeworks a semester

**Data Analysis: ** No

**Presentations: ** No

**Exams: ** One or two midterms and a final exam

**Keywords: ** Mathematical statistics. Statistical Inference theory.

**Comments: ** The sequence S721-722 is intended to prepare Ph.D students in the Department of Statistics for the theory portion of the qualifying exam.