Math 728: Statistical Theory

Terry Soo

MWF   01:00 -01:50 PM   SNOW 302 - LAWRENCE  

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:


Introduction to Mathematical Statistics (7th Edition), by Robert V. Hogg, Joeseph McKean, and Allen T Craig


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.    See the review sheet: math728rev.pdf.   Proofs will be an important part of the course.




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 

normality

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


HW2 (Due Feb 10): HW2 (version Feb 1)
Brief Solutions, with thanks to YanHao Cui

HW3 (Due Feb 17): HW3 (version Feb 10)       
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