About 18.655: Mathematical Statistics

Class Summary

18.655 is an introductory graduate course in theoretical statistics. Topics include:

• Statistical decision theory
• Exponential families
• Principles of data reduction
• Bayes and minimax estimation
• Hypothesis testing
• Maximum likelihood estimation
• Large sample theory
• Resampling methods
• and more!

Prerequisites

• Introductory statistics (at the level of 18.650 or equivalent)
• Basic probability (18.05 or equivalent)
• Real analysis (18.100 or equivalent)
• or instructor consent

Class Learning Objectives

From this class, you should

1. An understanding of how theoretical questions in statistics are framed
2. Understand the proof techniques and reasoning common in statistics

Resources

The course has one required textbook, "Theoretical Statistics: Topics for a Core Course" by Robert Keener. There is free online access through the MIT libraries: https://lib.mit.edu/search/bento?q=theoretical+statistics and click "View Online". Other useful references include

• E.L. Lehmann, G. Casella, Theory of Point Estimation
• E.L. Lehmann, J.P. Romano, Testing Statistical Hypotheses
• A. W. van der Vaart, Asymptotic Statistics
• M. Wainwright, High Dimensional Statistics

Lectures

All lectures will be held on Zoom. See the Module in Week 0 titled "Zoom Info" for the meeting information. Attendance in person is strongly recommended to ask questions and participate in the course. Recorded lectures will be posted to the course website after class.

Homework

The course will have weekly homework assignments posted each Friday and due the following Friday at 11:59 pm EST. Late homeworks will not be accepted, although the lowest homework score will be dropped from your grade. You are encouraged to work together on your homework, but all work submitted must be your own. You should also certainly ask the instructor for help on the assignments, and actively post questions on Piazza so everyone can collaboratively answer.

Exams

There will be two in-class midterm exams and no final exam for the course. During the exam periods, you will be expected to join the class Zoom call and work with your camera on. The exams are open book and open notes, but no collaboration between students is allowed. The lower midterm score will be dropped from your grade.

• Midterm 1: Oct. 21
• Midterm 2: Dec. 4

Participation

You are expected to come to lecture and participate in the course. Ask questions when you do not understand things and collaborate with each other when you are stuck, especially using the online tools.

Office hours

Office hours will be held on Zoom from 3-5pm ET on Wednesdays.

Grading Scheme 

The grading will consist of homework assignments (40%), two midterms (25% each), and participation (10%).