140.733.41
Statistical Theory III

Discontinued

Location
Internet
Term
3rd Term
Department
Biostatistics
Credit(s)
4
Academic Year
2024 - 2025
Instruction Method
Synchronous Online
Class Time(s)
M, W, 10:30 - 11:50am
Auditors Allowed
No
Available to Undergraduate
No
Grading Restriction
Letter Grade or Pass/Fail
Course Instructor(s)
Constantine Frangakis
Contact Name
Constantine Frangakis
Frequency Schedule
Every Year
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. Examine foundational concepts of statistical inference (continues from 732: approximating distributions when sample is large; estimators as solutions to unbiased equations; confidence intervals and hypothesis tests)
  2. Derive the normal approximation to the distribution of the maximum likelihood estimator of a scientific quantity
  3. Identify whether the normal approximation is expected to give accurate inference
  4. Formulate semiparametric models for regression problems without relying on normality and homoscedasticity; and derive consistent estimators, with approximate variance estimates, for the regression parameters
  5. Approximate the variance of functions of estimators
  6. 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
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)