# 140.733.01Statistical Theory III

Location:
East Baltimore
Term:
3rd term
Department:
Biostatistics
Credits:
4 credits
2022 - 2023
Instruction Method:
In-person
Class Times:
• M W,  10:30 - 11:50am
Auditors Allowed:
Yes, with instructor consent
No
Course Instructor:
Contact:
Constantine Frangakis
Resources:
Prerequisite:

Linear algebra; matrix algebra; real analysis; calculus; 140.731-2

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:

1. Derive the normal approximation to the distribution of the maximum likelihood estimator of a scientific quantity
2. Identify whether the normal approximation is expected to give accurate inference
3. Formulate semiparametric models for regression problems without relying on normality and homoscedasticity; and derive consistent estimators, with approximate variance estimates, for the regression parameters
4. Approximate the variance of functions of estimators
5. 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: