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Statistical Theory III

East Baltimore
3rd term
4 credits
Academic Year:
2022 - 2023
Instruction Method:
Class Times:
  • M W,  10:30 - 11:50am
Auditors Allowed:
Yes, with instructor consent
Undergrads Allowed:
Grading Restriction:
Letter Grade or Pass/Fail
Course Instructor:
Constantine Frangakis

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


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:

Special Comments:

Please note: This is the in-person section of a course that is also offered virtually/online. Students will need to commit to the modality for which they register. One 1-hour lab per week (time TBA)