## S721: Advanced Statistical Theory I

### Class Description

This course will cover the basics of probability theory necessary for and understanding of statistical inference (no measure theory). It focuses mainly on the material covered in Chapters 1--10 of Casella and Berger with additional material to supplement as time permits. This course should prepare students for more advanced courses in the statistics department as well as introduce them to a handful of modern theoretical tools useful for statistical research.

### Class Information

**Semester(s): **Fall

**Semester(s) Offered: ** Fall

**Class time: **
Tuesday, Thursday : 1:00-2:15

**Capacity: ** 15

### Contact Information

**Instructor: **Chunfeng Huang - haung48@indiana.edu

**Other Contact(s): ** Chunfeng Huang - haung48@indiana.edu

### Other Details

**Sequence: ** Stat-S 722 -- Advanced Statistical Theory II

**Prerequisites: ** Prerequisite of Stat-S 620 or consent of instructor. Math M-511, Econ-E571, would be sufficient. Content assumes comfort with calculus and previous exposure to probability at the Math-M463 level.

**Algebra Required?: ** Little to none.

**Calculus Required?: ** Used thoroughly.

**Day(s) per week offered: ** Currently taught twice weekly. No lab.

**Recommended follow-up classes: ** Any course offered by the department of statistics, Math M-563, Econ E-571/572/671 (overlaps with the material to some extent)

**Substantive Orientation: ** Informatics, Computer Science, Economics, Business, Math

**Statistical Orientation: ** theoretical

**Books used: ** Main text - Casella and Berger Statistical Inference, Others - Wasserman All of Statistics, Das Gupta Asymptotic Theory of Statistics and Probability

**Applied/Theoretical: ** theoretical, little to no application

**Software Used: **
NONE

**How the software is used: ** Occasional simulation, or compute the CDF/PDF of some random variable (could be done in anything)

**Problem Sets: ** Weekly

**Data Analysis: ** None

**Presentations: ** None

**Exams: ** Midterm and Final

**Keywords: ** Random variables, probability distributions, convergence concepts, concentration of measure, learning theory, estimators, hypothesis tests, confidence intervals, bootstrap, advanced theory.