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Statistical Theory II

East Baltimore
2nd Term
Academic Year
2022 - 2023
Instruction Method
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

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
Final grade applies to all terms
Special Comments

Please note: This is the onsite section of a course that is also offered virtually. Students will need to commit to the modality for which they register. One 1-hour lab per week (time TBA)