# 140.733.01Statistical Theory III

Location
East Baltimore
Term
3rd Term
Department
Biostatistics
Credit(s)
4
2024 - 2025
Instruction Method
In-person
Class Time(s)
M, W, 10:30 - 11:50am
Auditors Allowed
Yes, with instructor consent
No
Course Instructor(s)
Contact Name
Frequency Schedule
Every Year
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. 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
Multiterm
Final grade applies to all terms