## STAT-610: Introduction to Statistical Inference

Spring 2012, SMI 133, TR 11a-12:15p

Instructor:   Chunming Zhang, Prof., Office: 1155 Medical Sciences Center. Phone: (608)262-0084. E-mail: cmzhang_at_stat_dot_wisc_dot_edu.

TA:  Chandler Zuo. Office: 1130 MSC. Phone: (608)265-6217. E-mail: zuo_at_stat_dot_wisc_dot_edu. Office hour: TW 5-6p.

 Discussion Time Classroom 311 M 4-5:15p Sterling 1327

Requirements:    Stat 309 or Stat 431, Math 521, Math 340 or equiv or cons inst

Description:

This course sequence is designed for first year graduate students in statistics. The primary objective is to present important techniques and basic results of mathematical statistics at a rigorous but not advanced level. For Ph.D. students without extensive experience in mathematical statistics, this sequence serves as a natural statistical prerequisite to the advanced 709-710 mathematical statistics course. Furthermore, the sequence provides extensive and relevant coverage of mathematical statistics for M.S. students, at a level above the undergraduate 309-310 course. All students should have a solid calculus prerequisite, some exposure to basic probability and statistics, and some knowledge of linear algebra. The first semester course, 609, develops the probabilistic tools and language of mathematical statistics. The course describes numerous properties of random variables and vectors, common distributions and important large sample results. In the second semester, 610, the mathematical structure of statistical inference is studied. In particular, the theory of estimation, confidence sets, testing, and prediction in common parametric models is investigated.

Text and Other Materials:

Required textbook: Mathematical Statistics (2nd edition, Vol. 1) by Bickel and Doksum. Prentice Hall.

A list of errata will be provided.

Topics to be covered:

• Chapter 1: Statistical Models: Elements of Decision Theory. Bayesian Models. Prediction. Sufficiency. Exponential Models.
• Chapter 2: Methods of Estimation: Minimum contrast estimates. Estimating equations. Weighted least squares. Empirical plug-in estimates. Maximum likelihood.
• Chapter 3: Criteria: Minimax. Bayes. Unbiased. Information Inequality. Robustness.
• Chapter 4: Testing and confidence regions: The Neyman-Pearson Lemma. Uniformly most Powerful Tests. Monotone Likelihood Ratio Models. The Duality between Tests and Confidence Regions. Bayesian Formulations. Likelihood Ratio Procedures. Prediction Intervals.
• Chapter 5: Asymptotic approximations. Consistency. The Delta Method. Asymptotic Normality of Estimates. Asymptotic efficiency of the maximum likelihood estimate.
• Chapter 6: Inference for Gaussian Linear Models. Regression. Analysis of Variance. (If time permits.)
Homework:

Problems will be assigned at almost every class meeting and will be due at the start of lecture on Thursday of the week after it is assigned. For example, homework assigned on Tuesday 01/25 and Thursday 01/27 will be due on Thursday 02/03; the primary purpose of the discussion is to provide you with help in completing the homework. No late homeworks will be accepted. Homeworks will be graded and missed homeworks will receive a grade of zero. To receive credit on homework you must: show all work neatly, clearly label each problem, circle your final answers, staple your entire assignment together in the correct order with your name printed on each page; homeworks which violate these regulations will be given a grade of zero.

Homeworks will generally be graded on a scale of 100 points. Your semester average for the homeworks will count as 11% of your course grade.

You are allowed, and even encouraged, to work with other students on the homework problems. Copying of homework, however, is absolutely forbidden. Therefore each student must produce his or her own homework to be handed in and graded.

Exam:

There will be two in-class midterm exams, and an in-class final exam. Exams are closed book, but you will need to bring a calculator to each exam. All the exams are required, and there will be no make-up exams. An additional review session will be scheduled before each exam if time permits.

• You are allowed to bring 1 double-sided formula sheet (A4-sized, 11.00X8.50 in) in each exam (midterms, and final exam). The sheet is only for formulas related to this course; no extra sheets pasted on the formula sheet are allowed; problems and solutions are not permitted to be in the formula sheet. Before exams, the formula sheet will be checked by instructor and TA.
• The instructor and TA are not responsible for providing calculators during exams.
• There will be no makeup test for any test/exam missed. Students who missed their test will be given a zero score unless they can produce a valid medical/military certification for their absence.
• The final exam is cumulative.
• For students officially enrolling for "Honors credit", please see the instructor at the beginning of the semester (i.e., within the first two weeks). For students in other cases, no extra work/credit will count in computing the final grades.

Schedule:

 Event Date Weight Homework As assigned (to be announced) 11% Midterm 1 March 6 (Tuesday) 27% Midterm 2 April 17 (Tuesday) 27% Final Exam May 15 (Tuesday), 12:25PM - 2:25PM 35% Total 100%

Remark:

• If you have questions, you are strongly encouraged to ask in class or to stop by the instructor's office after the lecture. Thanks for your cooperation.
• The instructor will not respond to requests which she judges as "unreasonable".