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:
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:
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
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