# 140.732.71Statistical Theory II

## Course Status Cancelled

Location
Internet
Term
2nd Term
Department
Biostatistics
Credit(s)
4
2022 - 2023
Instruction Method
Synchronous Online
Auditors Allowed
No
No
Course Instructor(s)
Contact Name
Frequency Schedule
One Year Only
Resources
Prerequisite

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

Description
Introduces modern statistical theory; sets principles of inference based on decision theory and likelihood (evidence) theory; derives the likelihood function based on design and model assumptions; derives the complete class theorem between Bayes and admissible estimators; derives minimal sufficient statistics as a necessary and sufficient reduction of data for accurate inference in parametric models; derives the minimal sufficient statistics in exponential families; introduces maximum likelihood and unbiased estimators; defines information and derives the Cramer-Rao variance bounds in parametric models; introduces empirical Bayes (shrinkage) estimators and compares to maximum likelihood in small-sample problems.
Learning Objectives
Upon successfully completing this course, students will be able to:
1. Translate the design and estimation goal of a scientific study into a theoretically appropriate statistical framework
2. Identify appropriate parametric models for the population under study
3. Calculate the likelihood of the study’s data based on the design and model assumptions
4. Find the minimal sufficient statistics and the maximum likelihood estimator for the quantity of interest
5. Find Bayes/empirical Bayes estimators for a loss function and compare small-sample properties to those of the maximum likelihood estimator
Methods of Assessment
This course is evaluated as follows:
• 25% Homework
• 75% Final Exam