STA 701 Advanced Statistical Inference I

Fall Semester 2012

Class Instructor
Name: Mai Zhou
Address: 343 MDS
Telephone: 257-6912
Email: mai@ms.uky.edu
Office Hours : TBA and by appointment.

Course Information
Class time and place : Tuesday and Thursday 2:00 PM - 3:15 PM, at MDS 335. Final Exam: 
Lecture Notes: Van der Vaart, Mathematical Statistics, this is a 70 page notes, available online here .  PDF version
Some good notes from UMN here .  And a 500 page probability/Statistics book here and here.
Mai Zhou (1), Asymptotics for Maximum Likelihood, this is a 16 page notes, available here . Mai Zhou (2), Empirical Likelihood, will be available a bit later.
Other useful books for this class: Thomas Ferguson, Mathematical Statistics, A Decision Theoretic Approach, Academic Press. (Our topics for the April.)
A.W. Van der Vaart, Asymptotic Statistics, Cambridge University Press. (has much more than can be covered in one semester. Has a chapter on U-statistics.)
Website : This page will be updated regularly. Please keep checking it often for announcements and homework information.


Course Policies
Description: This is an advanced three credit hour course whose topics include but may not be limited to Asymptotics of the maximum likelihood inference method; M- and Z-estimators; optimality properties. basic concepts of decision theory, Bayes and minimax estimators; The course assumes familiarity with the materials encountered in STA 601 and, of course, STA 531 and STA 532.
Course Goals: Apart from the (self-evident) knowledge of the STA 701 topics, and in addition to emphasizing analytic and problem-solving skills and the ability to apply principles and generalizations already learned to new problems and situations, the course is intended to provide an environment in which a commitment to accurate work, the capacity to think creatively. It prepares you for future independent, original research in statistics.
Attendance: Consistent attendance is strongly recommended. Each student is responsible for obtaining all material missed when absent.
Grading: Your grade will be divided into 4 equal parts. Three exams, each worth 25% of your final grade, and the remaining 25% will be based on about weekly homework assignments.
The homework assignments and exams must be your own work. Late homework will not be accepted without a university excused absence (check out the details here).
Exams: Make-up exams will be allowed only in extreme circumstances and are subject to proper documentation. Unless it is an emergency situation, you need to notify me ahead of time either by phone or via email.

A page contain the probability results we have covered so far (Fall 2012).

Homework1   Homework2

Homework3    Final Exam: Final

Topics list. This is a list of topics we have covered in this class.  

Solution for 2008 Q7 here.

Notes: NPBaye
DirichletDist

Examples of MLE and confidence interval done in R

Below are From previous versions of sta701. No longer relavant.


Tentative Schedule

Date Topics Book Sections Handouts/Assignments
Thur, Jan 13 Introduction. Examples. Why asymptotics? AWV 1.1
Tues, Jan 18 Big O and small o AWV 1.2
Thur, Jan 20 Stachastic O and o AWV 1.2 Homework 1:
Tues, Jan 25 Multivariate Normal distribution AWV 2.1, 2.2
Thur, Jan 27 Homework 2:
Tues, Feb 1 Lindberg-Feller CLT, Cremer-Wold device AWV 2.3
Thur, Feb 3 Delta method AWV 3.1 Homework 3:
Tues, Feb 8 Delta method, examples AWV 3.2
Thur, Feb 10 Z and M estimators AWV 4.1
Tues, Feb 15 M estimators AWV 4.2, 4.3
Thur, Feb 17 Maximum Likelihood MZ1
Tues, Feb 22 Maximum Likelihood MZ1
Thur, Feb 24 Nonparametric estimation AWV 5.1 Homework 4:
Tues, Mar 1 Empirical distribution functions AWV 5.1/MZ2
Thur, Mar 3 Empirical likelihood. MZ2 Homework 5:
Tues, Mar 8 Empirical likelihood. MZ2
Thur, Mar 10 Exam
Tues, Mar 15 Spring Break - No Classes!
Thur, Mar 17
Tues, Mar 22
Thur, Mar 24 Limit of posterior distributions
Tues, Mar 29 Desicion theory Ferguson 1.1, 1.3, 1.5
Thur, Mar 31 Homework 7:
Tues, Apr 5 Bayes and minimax Ferguson 1.6, 1.8
Thur, Apr 7
Tues, Apr 12 geometric interpretations
Ferguson 1.7, 2.7
Thur, Apr 14 Solving for minimax rules Ferguson 2.11
Tues, Apr 19 Estimating normal mean Ferguson 3.7 Homework 8:
Thur, Apr 21 Complete Class Ferguson 2.3
Tues, Apr 26 Most powerful unbiased tests Ferguson 5.4
Thur, Apr 28 Reviews
Thur, May 5 Final Exam (8-10 AM)
Decision problem setup. Loss function. Risk function. Bayes risk.

Minimax rule. Admissible rule. Bayes rule for a prior distribution. (square error loss, absolute error loss) Extended Bayes rule. Equalizer rule. (Some examples of the above rules.)

Equalizer + Extended Bayes => Minimax.
Admissibility of Bayes rule.
Least favorable prior distribution. Minimax + infsup/supinf + LF prior exist => Bayes wrt LF prior

Geometric interpretations. Randomized rules. Convexity of Risk set.

prior and posterior for Binomial dist. Normal dist. (mean, and 1/variance) Poisson dist. Exponential dist.