__Math 728:
Statistical Theory__

Terry
Soo

Office hours, Monday 4-5, Friday 2-3.

In
this course we will cover core topics in statistical theory
such as: the consistency, efficiency, and sufficiency of
estimators; confidence intervals and hypothesis testing; and
Bayesian statisics. We will cover selected topics from
Chapters 4-11 of the required textbook:

This course will help students who are
preparing for the Probability and Statistics qualifying
exam.

**Prerequisites**: Math
727. I particular, students should be comfortable
with the material in Chatpers 1-3 of the textbook, the law
of large numbers, and the central limit
theorem.

**Grading**:

Homework: 20%

Midterm 1: 20% February 24 (coverage,
including Feb 18) solutions

Midterm 2: 20% April 6 solutions

Final Exam: 40% May 10
(10:30--1:00PM) solutions

Other references:

Statistical Inference, Casella and Berger

Mathematical Statisitics, Shao

Theory of Point Estimation, Lehmann and Casella

Testing Statistical Hypothesis, Lehmann and Romano

**Notes:
**

introduction

mle

mle consistent

fisherraocramer

suff

rao-blackwell

lehmann-complete

laplaceviaweierstrass

expclass

basu

CIandHyTmath526

hypoLRT

like

best

UMP

bayesI

bayesII

practice

**Homework
**

**
**HW1
(Due Jan 27): Do Exercises 1.1, 1.3, 2,7, 3.2, 4.3,
4.4, 4.5, 5.3, 5.4 from the review sheet, version Jan
20.

Brief solutions, with thanks to YanHao Cui

Brief Solutions, with thanks to YanHao Cui

solutions

HW4 (Due March 2): Do Exercises: 1.2, 1.5
(continuous case), 1.6, 1.8 (discrete case), 2.3, 2.4, 2.9 from
these notes: basiccondexp.
Also do Exercise 3.3, from the first review sheet.

Brief solutions, with thanks to YanHao Cui

HW5 (Due March 9): HW5 (version March
7)

Brief solutions, with thanks to YanHao
Cui

HW6 (Due March 23): HW6 (version March 2)

Brief solutions, with thanks to YanHao
Cui

HW7 (Due March 30): HW 7 (Version March 29)

solutions

HW8 (Due April 13): HW 8 (version April
12, Q2e omitted)

solutions

HW9 (Due April 27): Last HW

HW 9 (part I) (Version
April 13)

HW 9 (partII) (Version April 17)

solutionI

solutionII

R code

You will not be tested on R.

The very basic R code I showed in class was based on two extra-credit assignments I gave in a previous course; this is before I learned the `replicate' function, so my code has more `for loops' than necessary. I post here all the R-notes from that previous course and an example of the replicate function.

Rcodefolder