823-Large Sample Theory. (3) (Prerequisite: STAT 713) Modes of convergence, limit theorems, and the asymptotic properties of estimators and tests.
Course Homepage: Recent Semester
Usually Offered: Spring even years.
Purpose: The purpose of this course is to introduce students to the theory and application of large-sample methods. The emphasis of this course will be on applications, focusing largely on understanding and formulating large-sample arguments.
Current Textbook: Ferguson, T. A Course in Large Sample Theory. New York: Chapman & Hall, 1996.
|Review of analysis and probability theory||1.5 weeks|
|Modes of convergence||2 weeks|
|Central Limit Theorem (iid case), Approximation by averages||2 weeks|
|Delta Method, Slutsky's Theorem||1.5 weeks|
|Central Limit Theorem (non-iid case), bootstrap, Edgeworth expansions||1.5 weeks|
|Maximum likelihood estimation||2 weeks|
|Asymptotically optimal hypothesis tests||1.5 weeks|
The above textbook and course outline should correspond to the most recent offering of the course by the Statistics Department. Please check the current course homepage or with the instructor for the course regulations, expectations, and operating procedures.