140.733.41
Statistical Theory III

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:

cfranga1@jhu.edu

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 1-hour lab per week (time TBA)