SDS 4020 Mathematical Statistics

Instructor: Likai Chen (likai.chen[at]wustl.edu)

Lectures: Mon/Wed/Fri 1:00 PM-1:50 PM, MALLINCKRODT, Room 302

Office hour:

Schedule

Topics covered

Special Distributions, theory of estimation, minimum variance and unbiased estimators, maximum likelihood theory, Bayesian estimation, prior and posterior distributions, confidence intervals for general estimators, standard estimators and distributions such as the Student-t and F-distribution from a more advanced viewpoint, hypothesis testing, the Neymann-Pearson Lemma (about best possible tests), linear models, and other topics as time permits.

Prerequisites

The prerequisite is Math 493, Math 3200 and Math 318 (or Math 308), or equivalent mathematical maturity and experience.

Textbook

Robert Hogg, Joseph McKean and Allen Craig,
Introduction to Mathematical Statistics, 8th edition
Pearson Prentice Hall, 2018

Remarks:
Solutions to selected problems are in the back of the book.

Exams

There will be two midterms and one final. The final is scheduled at the end of the semester. All exams are closed book and closed note. One page (letter size and two-sided) note may be brought to exams. All the distribution tables will be provided by the instructor. Calculators are allowed but not required.

Make-up exams are strongly discouraged. If you are aware of a conflict, please inform the instructor before the exam. Make-up exam will only be given if (1) within 1 week of the standard exam and (2) suitable documentation is provided within 2 days.

Homeworks

There will be about 11 homework assignments throughout the semester. About 6 homework problems (may including computer homework problems) will be assigned each week and the solutions to all problems will be posted on the course website. Most of the exam and final questions will be similar to these. Hence you are strongly suggested to compare your answers with the posted solution. Weekly homework is due on Wednesday midnight. NO LATE HOMEWORK WILL BE ACCEPTED. One lowest grade of your hw will be dropped.

Grades

Your grade will be based on weekly homework, midterm and final exam.

Midterms 25% each
Final 30%
Homework 20%

The threshold for each grade

A A- B+ B B- C + C C -
90 or above89-90 87-89 80-87 78-80 76-78 62-76 60-62
Only very few top students will get A+.

Software

Open-source software R for statistical computing, and its manual .
Download R from Wustl's software.
Download R Studio from its developer's website.