S721: Advanced Statistical Theory I
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.
Semester(s) Offered: Fall
Class time: Tuesday, Thursday : 1:00-2:15
Instructor: Chunfeng Huang - firstname.lastname@example.org
Other Contact(s): Chunfeng Huang - email@example.com
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
Exams: Midterm and Final
Keywords: Random variables, probability distributions, convergence concepts, concentration of measure, learning theory, estimators, hypothesis tests, confidence intervals, bootstrap, advanced theory.