## STAT 610a, Statistical Inference

### Fall 2005

Instructor: Harrison H. Zhou.
e-mail: huibin.zhou@yale.edu.
Office hours: Monday and Wednesday 10:30-11:30, or by appointment

Class Time: Tuesday, Thursday 10:30-11:45, 24 Hillhouse Avenue, Room 107. An informal recitation class will be offered at 6:15-7:00 on Wednesday.

T.A.: Cong Huang (cong.huang@yale.edu).

Textbook: Erich Lehmann and George Casella, ``Theory of Point Estimation''.
We will cover core material from chapters 1 through 6.

Weekly Homework: 45%
Midterm: 15%
Final Exam: 30%
Participation: 10%

Course Description: A systematic development of the mathematical theory of statiscal inference focussing on optimality in estimation: Best unbiased, best invariant, minimax, Bayes, admissibility, efficiency, asymptotics.

Course Homepage: http://www.stat.yale.edu/~hz68/610/

Homeworks
HW1 : Chapter 1: Problems 1.2, 1.8, 4.1, 4.13, 5.1 Due Thursday Sept 8 in class. Homework 1
HW2 : Chapter 1: Problems 5.6, 5.7, 5.25, 6.1, 6.3 Due Friday Sept 16
HW3 : Chapter 1: Problems: 6.6, 6.7, 6.16, 6.29, 6.31(a) Due Friday Sept 23
HW4 : Chapter 1: Problems: 6.35, 6.36, 7.9; Chapter 2: 1.15 Due Thursday Sept 29
HW5 : Chapter 2: 1.12, 1.18, 1.20, 2.8, 2.19, 2.24 Due Friday Oct 7
HW6 : Chapter 2: 5.3, 5.9, 5.13, 5.22, 5.27 Due Friday Oct 14
HW7 : Chapter 3: 1.6, 1.11, 3.6, 3.10 Due Friday Oct 21
Midterm Exam
HW8 : Chapter 4: 1.1, 2.8 Due Friday Oct 28
HW9 : Chapter 4: 2.15(a, b), 3.3, 3.4, 4.4, 7.1a, 7.3a
HW10: Chapter 5: 5.4, 5.7(a,b), 6.1.
HW11: Chapter 5: 1.9, 1.21, 2.9 (a, b, c), 7.14, 7.15.
Note: (i) for part (c) of 2.9, you could just prove a weaker version of the result by replacing " for m<1/sqrt(n) ... " with " there is a positive constant m_0, independent of n, such that ...". There is a typo in this part, please replace max{R(-m,...),...} by max{R(0,...),...}
(ii) For problem 7.14, there are four parts, but at least one part of the problem is not right. Your job is to find the first wrong part and explain it.
(iii) The statement of problem 7.15 may not be right. So if you can not get an admissibilty result, try to show that the estimator is inadmissible.
Final Exam
Due 2:30pm, Dec 9th.