Spring 2017

TR 01:00 -02:15 PM SNOW 302

January 17 -- May 4.

See this link for the KU calendar year.

Terry Soo, Snow 610

Office hours: Tuesday 2:30 - 3:30. Friday 2-3.

Course description.

In this course we will cover core topics in point estimation, hypothesis testing, and Bayesian statistics. Highlights include the Cramer-Rao bound, the Rao-Blackwell theorem, the Lehmann-Scheffe theorem and the Neyman-Pearson lemma.

In particular, students should be comfortable with conditional expectation, the law of large numbers, and the central limit theorem.

Other suitable references are:

Introduction to Mathematical Statistics, Hogg, McKean, and Craig. (Used last year)

Statistical Inference, Casella
and Berger (Used in previous years)

Mathematical Statisitics, Shao

Theory of Point Estimation, Lehmann and Casella

Testing Statistical Hypothesis, Lehmann and Romano

This course will also have a minor computing component. We will have the chance to use the free statistical software R. It can be downloaded here. A short introduction to R can be found here. Knowledge of R will not be required on examinations. However, there may be a few R homework assignments.

Homework: 30%. (Either weekly or biweekly)

Midterm 1: 10%. February 14 M1 sol

Midterm 2: 10%. March 14 sol

Midterm 3: 10%. April 20 sol

Final examination: 40%. May 12: 1.30 -- 4.00 PM registrar information

sol

Introduction

Maximum likelihood estimatation

Fisher information and the Cramer-Rao Bound

Central limit theorem for mle

Sufficient statistics

Change of variables

Conditional Expectation

Rao-Blackwell

Complete statistics

Laplace transforms

Exponential class

Basu

Higher dimensions

Introduction to R, sample code

The EM algorithm

Intro BayesI

Intro BayesII

Undergraduate hypothesis testing and confidence intervals

Introduction to Hypothesis testing and the LRT

Neyman-Pearson lemma for best tests

Uniformly most powerful tests and monotone likelihood ratios

Homework.

Homework 1: Due January 31

solution

Comments:

Updated Question 1; it is a better question now and also added the missing assumption of independence.

For Question 2, you do not need to know anything fancy about the distribution of a sum of independent uniforms, the reason being is that you only need to know the cdf of the sum up to value 1, and no more no less. Use induction.

For Question 5b, there was a missing term in the event, this is now corrected.

For Question 5e, there was a typo, it should have said Zk = Finverse(Vk); this has been corrected in the pdf file.

For Question 7, the pdf for the multivariate normal is provided.

I encourage you to typeset your solutions using LaTeX. For you reference here is a LaTex file that can be used to generate this homework .

latexfile. (Texfiles will not be updated)

Homework 2: Due February 7

solution

latexfile

Comments: In Question 1, there should be a negative sign was missing in one of the equations that defined symmetric. This has been corrected.

There was a typo in the solution to Exercise 5. This did not effect the final answer and has been corrected. See the remark in the solutions for details.

Homework 3: Due February 16

solution

latexfile

Homework 4: Due February 28

solution

latexfile

Homework 5: Due March 7

solution

latexfile

Homework 6: Due Monday March 13 3PM

solution

latexfile

Comments:

In Exercise 2, the definition of T is the sample sum; this was left out in the previous version, and is now corrected.

Homework 7: Due April 11

texfile

solution

Homework R: Due April 25

texfile

Comments: There should be a negative sign in the exponent in Ex4a.

Homework 9: Due April 18

texfile

solution

Last HW: Due May 4

texfile

solution

Comments:

In the first question, the assumption of symmetry in M is not necessary, all that you need is that it has zero median.