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Statistical Theory III

3rd Term
Academic Year
2022 - 2023
Instruction Method
Synchronous Online
Class Time(s)
M, W, 10:30 - 11:50am
Auditors Allowed
Available to Undergraduate
Grading Restriction
Letter Grade or Pass/Fail
Course Instructor(s)
Contact Name
Frequency Schedule
Every Year

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
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)