Math 494: Mathematical Statistics - Spring 2018

Instructor: Jimin Ding; 

Office: Cupples I, Room 112A;
Email: jmding@wustl.edu
TA/Grader: Jiayi Fu (email: jiayi.fu@wustl.edu), Jiahui Lyu(email: jiahuilyu@wustl.com)

Office Hours: Wed. 3:10-4:30pm. Friday 12:45-1:50pm. or by appointment.
TA office hour: Cupples I, Room 199, Thursday 2:30-3:30pm..

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. Please take a look at the schedule and exams of Math 493. If you can independently solve all the problems in the exams, you should be qualified.

Textbook:

Robert Hogg, Joseph McKean and Allen Craig,
Introduction to Mathematical Statistics, 7th edition
Pearson Prentice Hall, 2012,   ISBN 978-0-13-008507-8
eTextbook ISBN: 978-0-321-79543-4


Remarks:


• Solutions to selected problems are in the back of the book.
  
• We will cover selected topics from Chapters 4-11. Detailed schedule will be updated periodically on the course website.
• The 7th edition of the textbook is different from the order (the 6th) edition. The major changes are in chapter 4, which contains the old chapter 4 and the basic statistical inferences from the old chapter 5, and chapter 10, which contains old chapter 10 and the dicussion of robustness concepts from the old chapter 12. Our homework assignments will be based on the 7th edition.
• Course reserved desk copies of the textbook (both 6th and 7th edition) and reference books are available in Olin library for 1 day use.

Reference Books:

• Statistical Inference, 2nd ed.,, George Casella and Roger L. Berger, Duxbury Thomson Learning, Learning, 2002.
  
• All of Statistics: A Concise Course in Statistical Inference, Larry Wasserman, Springer, 2004.
  
• Applied multivariate statistical analysis, 6th ed., Richard A. Johnson, Dean W. Wichern., Prentice Hall, 2007.
  

Exams:

There will be two in-class midterms on Feb. 23 (Fri.) and Apr. 6 (Fri.) respectively and a final exam at 3:30-5:30pm. on May 7 (Mon.). Midterms are not accumulative, but the final exam is comprehensive. All exams are closed book and closed notes, and you may need a calculator for them. For each exam, at least 60% of the questions will be similar with, if not exactly same as, the homework questions, and 30% will be close to the examples discussed in class.

All exams are close-notes-and-close-book. No web-enabled devices may be used. One page (letter size and one-sided) note may be brought to each midterm, and all previous midterm notes plus one page additional note may be brought to the final exam. 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 11 homework assignments throughout the semester. The lowest homework grade will be dropped. About 6 homework problems (may including computer homework problems) will be assigned each week. The solutions to all problems will be posted on the course website (bb.wustl.edu), although only three of them will be graded and account toward your course grade. Most of the exam and final questions will be chosen from these problems with slight modifications. The rest of the exam questions will be similar to these. Hence you are strongly suggested to compare your answers with the posted solution.

Weekly homework is due on Friday 2pm. NO LATE HOMEWORK WILL BE ACCEPTED. Please label questions and write your work clearly. You are encouraged to produce printed homework using Latex or Word. You will receive no credits for solutions with no work or justifications. The instructor reserves the right to deduct points for messy papers.

Homework collection via crowdmark: Only PDF and JPEG format are accepted.

You will receive a link in email to submit your homework on crowdmark. After you finish homework, you need to upload your work for each homework question separately. Simply drag and drop your files to the upload areas under the questions or browse to locate them. You can drag pages between questions, and add or delete more pages under each questions. Please DO NOT upload your entire file to all homework questions, but only keep the related pages to each question. If you upload pictures of your homework, please make sure your pictures are sharp enough to be graded. Please ensure the uploaded pages are in order and rotated correctly.

After your work is graded, you will receive another link in email to review your score and grading comments.

Grades:

Your grade will be based on weekly homework, 2 midterms and final exam. Then your final letter grade is determined as follows. The A range will be 85 to 100, the B range will be 75 to 85, the C range will be 65 to 75, and the D range will be 60 to 65, with plus and minus grades given to the top 10% and bottom 10% students in each of these ranges. (If you register for ``Credit/No Credit'' or " Pass/Fail", Cr or P means D or better.)

Midterm exams	20% each
Final exam	30%
Homework	30%

Collaboration:

Collaboration on homework is allowed and can be helpful (and fun). However, you must do all written work by yourself, both answers to homework questions and computer programs. If you collaborate with someone on a homework, list his or her name in a note at the top of the first part of your homework. There should be NO COLLABORATION on exams. Following "the academic integrity policy", academic misconducts and dishonesty will be reported to the university academic integrity office and seriously affect the grade.

Attendance:

Class attendance is strongly encouraged. Experience has shown that students who attend class regularly perform better on average. Lectures will involve discussion of topics and usually help students understand the material. Completing the reading assignments is not a substitute for attending lecture, nor is attending lecture a substitute for competing the reading assignments.

Good books for reviewing elementary statistics:

• A Data-Based Approach to Statistics,R. L. Iman, Duxbury Press, 1994.
  
• Statistics and Data Analysis from Elementary to Intermediate, A. J. Tamhane and D. D. Dunlop, Prentice-Hall, 2000.
  
• Design and analysis of experiments, 2nd ed., Douglas Montgomery, John Wiley & Sons, 1984. (Good for multiple-comparison procedures.)
  
• Applied Linear Statistical Models, 4th ed., John Neter, M. Kutner, C. J. Nachtsheim, and W. Wasserman, Irwin/McGraw Hill, 1999.
  
• Applied Multivariate Statistical Analysis. 5th ed., R. A. Johnson and D. W. Wichern, Prentice Hall, 2002.