Math 728: Statistical theory.
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.
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.
Prerequisites: Math 727.
In particular, students should be comfortable with
conditional expectation, the law of large numbers, and the
central limit theorem.
be an important part of the course. Students
should be comfortable with reading and writing
This is a graduate course.
the review sheet: math728rev.pdf.
Textbook and lecture notes.
No textbook is required. We will follow course lecture
notes which can be found here,
which is the course website for 2016. Previous homework
assignments and exams are also available there. Lecture
notes will be updated and supplemented, and posted at this
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.
This course will help students who are preparing for the
Probability and Statistics qualifying examination, and requires a
high level of mathematical maturity.
Subject to revision.
Homework: 30%. (Either weekly or biweekly)
Midterm 1: 10%. February 14 M1 sol
Midterm 2: 10%. March 14 sol
Midterm 3: 10%. April 20
Final examination: 40%. May 12: 1.30 -- 4.00 PM registrar
Notes. Also see last year's notes, here
Maximum likelihood estimatation
Consistency of mle
Fisher information and the Cramer-Rao Bound
theorem for mle
Change of variables
Introduction to R, sample code
The EM algorithm
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 1: Due January 31
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
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
latexfile. (Texfiles will
not be updated)
Homework 2: Due February 7
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
Homework 4: Due February 28
Homework 5: Due March 7
Homework 6: Due Monday March 13 3PM
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
Homework R: Due April 25
Comments: There should be a negative sign in the exponent in Ex4a.
Homework 9: Due April 18
Last HW: Due May 4
In the first question, the assumption of symmetry in M is not necessary, all that you need is that it has zero median.