using tools of advanced calculus and basic analysis. The objectives are to treat

diverse statistically interesting models for data in a conceptually unified way; Homework Assignments.

to define mathematical properties which good procedures of statistical inference

should have; and to prove that some common procedures have them. Homework Solutions.

**Prerequisite:** Stat 700 or {Stat 420 and Math 410}, or equivalent.

**Text:** *(Required)* George Casella and Roger Berger
*Statistical Inference*, 2nd ed., Duxbury, 2002.

*(Recommended)*
V. Rohatgi and A.K. Saleh, *An Introduction to Probability and Statistics*,
2nd ed., Wiley, 2001.

Jun Shao, * Mathematical Statistics*, 2nd ed., Springer, 2003.

P. Bickel & K. Doksum *Mathematical Statistics, vol.I, 2nd ed.*, Pearson Prentice Hall, 2007.

P. Billingsley,
* Probability and Measure*, 2nd (1986) or later edition, Wiley.

**A sheet of errata in Casella & Berger compiled by Jeffrey Hart of
Texas A&M Stat Dept can be found here.
The most important of these errata are the ones on p.288, in Equation (6.2.7) and in line 14
(the last line
of Thm. 6.2.25): what is important as a sufficient condition for completeness is that the set of
"natural parameter" values (η**

**Course Coverage:** Last fall, Stat 700 covered the Casella & Berger through Sec.8.2.2, omitting
primarily the topics involving large-sample asymptotics. This term, we begin with Sections 5.5.3 and
5.5.4, then discuss asymptotic topics related to the comparison of large-sample variances of method
of moments and ML estimators (Chapter 7, Sec.2). We will re-visit the topic of
multidimensional-parameter) Fisher Information along with numerical maximization of likelihoods, via
Newton-Raphson, Fisher scoring, and EM algorithm. We complete this part of the course by proving that
MLE's under regularity conditions are consistent and asymptotically normal, with related facts about
the behavior of the Likelihood in the neighborhood of the MLE. For rigorous development of this
material, we follow roughly the development of Chapter 5 of the book of Bickel and Doksum, although
this material is covered non-rigorously in the univariate case in Casella and Berger's Section 10.1.

Next we return to the material not covered last term in Chapters 8 (Hypothesis Testing) and
9 (Confidence Intervals), incorporating large-sample asymptotics through the notions of
asymptotic size and power, asymptotically pivotal quantity, and asymptotic confidence level.
Likelihood ratio testing in composite-parameter settings will be covered in some detail,
following Section 8.2.1 for the finite-sample ideas. The asymptotic aspects of all of these topics
are introduced in Chapter 10 of Casella-Berger, but done more comprehensively in Bickel and Doksum's
Chapter 5 and 6, the latter covering multidimensional parameters and the relation between Wald tests,
score tests, and likelihood ratio tests.

In Casella and Berger, we cover through the end of Chapter 10, and in Bickel-Doksum,
Chapters 5-6 including some discussion of misspecified models, `M-estimation', and
estimating equations. Additional topics to be covered include: the Bootstrap
and its relation to the estimation of variances and confidence intervals; Bayes and empirical Bayes
methods including a brief introduction to Markov Chain Monte Carlo computational methods. All of these
topics not covered in Casella-Berger or Bickel-Doksum are included in the book of Shao, but some of
these topics are covered in this course primarily through handouts.

Lecture Topics by Date.

**Grading:** There will be graded homework sets roughly every 1.5--2 weeks (7 altogether).
There will be two in-class

tests, the first on Monday March 2, covering material through
the proofs about MLE asymptotics, the second tentatively

scheduled for April 29, and an in-class
Final Exam. The course grade will be based 30% on homeworks, 40% on tests,

and 30% on the Exam.

**No Test make-ups will be offered. Homework will generally not be accepted late, and must
be handed in as hard-copy (except for people off-campus when the due-dates are Fridays,
from whom electronic-format HW will be accepted as email attachments).**

HONOR CODE

The University of Maryland, College Park has a nationally recognized
Code of Academic Integrity, administered by the Student Honor Council.
This Code sets standards for academic integrity at Maryland for all
undergraduate and graduate students. As a student you are responsible
for upholding these standards for this course. It is very important for
you to be aware of the consequences of cheating, fabrication,
facilitation, and plagiarism. For more information on the Code of
Academic Integrity or the Student Honor Council, please visit
http://www.shc.umd.edu.

To further exhibit your commitment to academic integrity, remember to
sign the Honor Pledge on all examinations and assignments:

"I pledge on
my honor that I have not given or received any unauthorized assistance
on this examination (assignment)."

**Office Hours:** My office hours will be Monday 4-5 and Wednesday 11-12.
I will often be available also at other times,

except on Tuesdays and Thursdays,
but please send an e-mail or arrange with me in
class for an office appointment.

Also: messages and updates (such as corrections to errors in stated homework problems

or changes in due-dates) will generally be posted here, on this web-page, and only in

rare cases will be made through emails in the course "Reflector" account, which is

stat701-0101-spr15@coursemail.umd.edu

comments or questions that the whole class will see, and which I will answer in the same way.

Additional information: timing of individual
lectures and tests;
Important Dates below;

for auxiliary reading, several useful
handouts that are described and linked below;

cumulatively updated copy of all homework problem assignments;

partial problem set solutions
posted throughout the term.

**(I)** A handout on conjugate priors for
a class of exponential family densities and probability mass functions.

**(II)** Handout on
EM Algorithm from STAT 705.

**(III)** Lecture Notes from Stat 705 on Numerical Maximization of
Likelihoods. Some further steps in **R** showing

numerical maximization
of a Gamma likelihood can be found in this class handout.

**(IV)** Union-Intersection
Tests covered in Casella and Berger are
discussed in a journal article in

connection with applications to so-called
**Bioequivalence trials**.

**(V)** Summary of calculations in R comparing three
methods for creating (one-sided)

confidence
intervals for binomial proportions in moderate sized samples.

**(VI).** Handout containing single page Appendix from Anderson-Gill article
(Ann. Statist. 1982)

showing how uniform law of large numbers for
log-likelihoods follows from a pointwise strong law.

**(VII).** Handout on the 2x2
table asymptotics covered in a 2009 class concerning different
sampling

designs and asymptotic distribution theory for the log
odds ratio.

**(VIII).** Handout on Wald, Score
and LR statistics covered in class April 10 and 13, 2009.

**(IX).** Handout on Chi-square
multinomial goodness of fit test.

**(X)** Handout on Proof of
Wilks Thm and equivalence of corresponding chi-square statistic
with

Wald & Rao-Score statistics which will complete the proof
steps covered in class.

**(XI) Background on Markov Chain Monte Carlo:** First see
Introduction and application of MCMC

within an EM estimation problem
in random-intercept logistic regression. For additional pdf files of

"Mini-Course" Lectures, including computer-generated figures, see Lec.1 on Metropolis-Hastings
Algorithm,

and Lec.2 on the
Gibbs Sampler, with Figures that can be found in
Mini-Course Figure Folders.

**(XII).** A DIRECTORY OF SAMPLE PROBLEMS FOR old IN-CLASS FINAL (with
somewhat different

coverage) CAN BE FOUND HERE.
Similarly, SAMPLE FOR old IN-CLASS TESTS CAN BE FOUND HERE
.

A handout of topics and sample problems given for the
March 31, 2014, in-class test, can be found
here.

** Other handout topics from Stat 700,
including Sample Problems and Tests on Stat 700 topics, Distributions **

determined by moments, Mixture and models, Topics on Statistical Simulation.