140.733.41
Statistical Theory III
 Location:
 Internet
 Term:
 3rd term
 Department:
 Biostatistics
 Credits:
 4 credits
 Academic Year:
 2022  2023
 Instruction Method:
 Synchronous Online
 Class Times:

 M W, 10:30  11:50am
 Auditors Allowed:
 No
 Undergrads Allowed:
 No
 Grading Restriction:
 Letter Grade or Pass/Fail
 Course Instructor:
 Contact:
 Constantine Frangakis
 Resources:
 Prerequisite:
Linear algebra; matrix algebra; real analysis; calculus; 140.7312
 Description:

Derives the large sample distribution of the maximum likelihood estimator under standard regularity conditions; develops the delta method and the large sample distribution of functions of consistent estimators, including moment estimators; introduces the theory of estimation in semiparametric regression models based on increasing approximation of parametric models; develops likelihood intervals and confidence intervals with exact or approximate properties; develops hypothesis tests through decision theory.
 Learning Objectives:

Upon successfully completing this course, students will be able to:
 Derive the normal approximation to the distribution of the maximum likelihood estimator of a scientific quantity
 Identify whether the normal approximation is expected to give accurate inference
 Formulate semiparametric models for regression problems without relying on normality and homoscedasticity; and derive consistent estimators, with approximate variance estimates, for the regression parameters
 Approximate the variance of functions of estimators
 Derive confidence intervals/joint confidence regions and tests for quantities of interest, robust to assumptions of normal approximations
 Methods of Assessment:
This course is evaluated as follows:
 25% Homework
 75% Final Exam
 Instructor Consent:
Consent required for some students
 Consent Note:
Consent required for any students who are not in the Biostatistics PhD program
 For consent, contact:
 Special Comments:
Please note: This is the virtual/online section of a course that is also offered onsite. Students will need to commit to the modality for which they register. One 1hour lab per week (time TBA)