140.733.01
Statistical Theory III
Location
East Baltimore
Term
3rd Term
Department
Biostatistics
Credit(s)
4
Academic Year
2024 - 2025
Instruction Method
In-person
M, W, 10:30 - 11:50am
Auditors Allowed
Yes, with instructor consent
Available to Undergraduate
No
Grading Restriction
Letter Grade or Pass/Fail
Course Instructor(s)
Contact Name
Frequency Schedule
Every Year
Resources
Prerequisite
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:
- 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)
- Derive the normal approximation to the distribution of the maximum likelihood estimator of a scientific quantity
- Identify whether the normal approximation is expected to give accurate inference
- Formulate semiparametric models for regression problems without relying on normality and homoscedasticity; and derive consistent estimators, with approximate variance estimates, for the regression parameters
- Approximate the variance of functions of estimators
- 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
Final grade applies to all terms
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)