Mathematical Statistics

Course information

Instructor: Jonathan Niles-Weed (jnw@cims.nyu.edu)

Teaching Assistants:

• Alex Ding (yding@nyu.edu)
• Tim Kunisky (kunisky@cims.nyu.edu)

Description

The goal of this course is to develop mathematical tools for analyzing statistical procedures.

Prerequisites

Probability, linear algebra, mathematical maturity (comfort with proofs)

Books

While there is no required textbook, a portion of the material for this class will be drawn from All of Statistics by Larry Wasserman.

While this course will attempt to be rigorous where possible, several mathematically tricky issues will be ignored. A more rigorous treatment of some of the topics we cover is available in:

• Theoretical Statistics by Robert W. Keener
• Mathematical Statistics by Jun Shao

All three books are available for free via the links above with NYU credentials.

Announcements

Please sign up on Piazza

Schedule

Lecture notes will be written for each week’s lectures. Do not print them out, since they will be updated continuously throughout the semester. The homework assignments will be drawn from the list of exercises at the end of each chapter. Homeworks are due Thursdays at 11:59 pm, anywhere on earth.

Lectures

The following approximate schedule will be updated throughout the semester.

• Week 1 (9/3): Concentration inequalities. Video lectures: Part 1, Part 2, Part 3
• Week 2 (9/10): Uniform convergence. Video lectures: Part 1, Part 2, Part 3
• Week 3 (9/17): Statistical models, sufficiency, likelihood. Video lectures: Part1, Part 2, Part 3
• Week 4 (9/24): Point estimation (MLE, method of moments, M-estimators). Video lectures: Part 1, Part 2, Part 3
• Week 5 (10/1): Decision theory. Video lectures: Part 1, Part 2, Part 3
• Week 6 (10/8): Hypothesis testing, Neyman-Pearson Lemma. Video lectures: Part 1, Part 2, Part 3
• Week 7 (10/15): Goodness-of-fit, asymptotic and exact tests. Video lectures: Part 1, Part 2, Part 3
• Week 8 (10/22): Multiple testing. Video lectures: Part 1, Part 2, Part 3
• Week 9 (10/29): Confidence sets. Video lectures: Part 1, Part 2, Part 3
• Week 10 (11/5): Linear regression. Video lectures: Part 1, Part 2a, Part 2b, Part 3
• Week 11 (11/12): High-dimensional linear regression. Video lectures: Part 1, Part 2, Part 3
• Week 12 (11/19): Generalized linear models. Video lectures: Part 1, Part 2, Part 3
• Week 13 (12/3): Model selection. Video lectures: Part 1, Part 2, Part 3
• Week 14 (12/10): Nonparametric estimation. Video lectures: Part 1, Part 2, Part 3

Homeworks

• HW 1 (due 9/10): Chapter 1, Exercises 1-6
• HW 2 (due 9/18): Chapter 2, Exercises 1-4
• HW 3 (due 9/24): Chapter 3, Exercises 1-5
• HW 4 (due 10/1): Chapter 4, Exercises 1-5
• HW 5 (due 10/8): Chapter 5, Exercises 1-5
• HW 6 (due 10/22): Chapter 6, Exercises 1-3; Chapter 7, Exercises 1-3
• HW 7 (due 10/29): Chapter 8, Exercises 1-4
• HW 8 (due 11/5): Chapter 9, Exercises 1-5
• HW 9 (due 11/12): Chapter 10, Exercises 1-5
• HW 10 (due 11/19): Chapter 11, Exercises 1-5
• HW 11 (due 12/3): Chapter 12, Exercises 1-4

Exams

• Midterm released October 15, due October 16 @ 11:59 pm anywhere on earth
• Final released December 17, due December 18 @ 11:59 pm anywhere on earth. Practice final, Final exam

Logistics

Our class will be blended, offering both in-person and online content.

Video lectures

One-hour video lectures will be posted each week by Monday. Please watch these lectures each week before Wednesday.

Live lecture

Thursday 11am-12pm (Zoom)

The in-person lecture will offer addition context and material related to the video lectures. It will not duplicate material from the video lecture.

Recitation

Wednesday 12pm-12:50pm

• Alex: Virtual (Zoom link on Piazza)
• Tim: Virtual (Zoom)

Office Hours

• JNW: Thursdays 8-9am Eastern time, 4-5pm Eastern time (Zoom)
• AD: Mondays 1-2pm Eastern time (Zoom link on Piazza)
• TK: Tuesdays 11 am–noon Eastern time (Zoom)

Grading

40% Homework + 20% Midterm + 20% Final + 20% Participation/effort

Homework

There will be approximately 10 homework assignments over the course of the semester. The lowest homework score will be dropped.

You are encouraged to work with other students, however you must a) write solutions to the homework yourself and b) list the names of the students you collaborated with. If you consult any other sources (printed or online), you must cite those in your homework as well. Any violation of these policies will be considered cheating.

Midterm & Final

There will be a midterm exam and a final. You will be given 24 hours to complete the exam, though it will be designed to take about 90 minutes. You may use your notes and the course lecture notes, but you may not consult with other students or use any other sources. Any violation of these policies will be considered cheating.

Participation & Effort

This semester offers a unique challenge for all of us. In recognition of the strangeness of the semester, I will be giving you many opportunities to earn a good grade. In particular, you can earn up to 20% of your grade by showing good effort in the course. This can include:

• asking good questions on Piaza
• asking good questions in office hours
• answering questions from other students on Piaza
• actively participating in recitations and in-person lectures, where possible
• displaying clear and consistent effort on homework assignments

Cheating

NYU policy prescribes strong punishments for students caught cheating. The course staff will be carefully monitoring assignments and exams for signs of academic dishonesty.