Mathematical Statistics

Course Objective: This course aims to give an introduction to mathematical statistics with applications. Prerequisites include calculus, linear algebra, and probability at the undergraduate level.

Instructor:

  • Lecture: Shuyang LING (sl3635@nyu.edu)

  • Recitation leader: Yuntian YE (yy1947@nyu.edu)

Time/Location:

  • Lecture: 1:15PM - 2:30PM on Mondays and Wednesdays, Shanghai time, PDNG 204

  • Recitation: 1:15PM - 2:30PM on Fridays, Shanghai time, PDNG 211

  • Both sessions are available on Zoom via NYU Class.

Office hours:

  • Shuyang Ling, Room 1162-3, 10AM - 11AM on Wednesdays, also available on Zoom

  • Yuntian Ye, TBD

Textbook:

  • All of Statistics: A Concise Course in Statistical Inference by Larry Wasserman. It is available free of charge on Springerlink if you are connected to the NYU wireless networks.

  • Statistical Inference, 2nd Edition by George Casella and Roger L. Berger. It is available on Amazon.com. This is a classic textbook on statistical inference, covering essential parts of statistical inference in depth.

  • Probability and Statistics, 4th Edition by Degroot and Schervish.

  • Applied Linear Regression Models, 4th Edition by Kutner, Nachtsheim, and Neter.

Course schedule: The slides will be updated after each lecture. The full lecture notes are here, which are based on the four textbooks above.

Date Topics
Sep 14 (M) Probability
Sep 16 (W) Probability
Sep 21 (M) Limiting theorem
Sep 23 (W) Introduction to stats
Sep 28 (M) Evaluation of point estimators
Sep 30 (W) Estimation of CDF
Oct 05 (M) Bootstrap
Oct 07 (W) Method of moments
Oct 12 (M) Maximum likelihood estimation
Oct 14 (W) Maximum likelihood estimation
Oct 19 (M) Maximum likelihood estimation
Oct 21 (W) Delta metod and Cramer-Rao inequality
Oct 28 (W) Midterm
Oct 30 (F) Multi-parameter inference
Nov 01 (U) Multi-parameter inference
Nov 02 (M) Hypothesis testing
Nov 04 (W) Hypothesis testing
Nov 09 (M) Wald test and p-value
Nov 11 (W) Likelihood ratio test
Nov 16 (M) Goodness-of-fit tests
Nov 18 (W) Regression
Nov 23 (M) Simple linear regression
Nov 25 (W) Normal error model
Nov 30 (M) Multiple linear regression
Dec 02 (W) Multiple linear regression
Dec 07 (M) Model diagnostics
Dec 09 (W) Logistic regression
Dec 14 (M) Logistic regression