SAMPLE PROBLEMS FOR IN-CLASS FINAL CAN BE FOUND HERE.
SAMPLE FOR IN-CLASS TEST CAN BE FOUND HERE.
Take-Home TEST due May 11 CAN BE FOUND HERE.
The
solutions can now be found here.
This course introduces mathematical statistics at a theoretical
graduate level, using tools of advanced calculus and basic analysis.
The objectives are to treat diverse statistically interesting models for
data in a conceptually unified way; to define mathematical properties which
good procedures of statistical inference should have; and to prove that
some common procedures have them.
In the Spring term, (Stat 701), we begin by studying topics relatd to
(finite-sample) hypothesis testing and confidence regions, but for the
rest of the semester we will emphasize large-sample theory results,
especially the large-sample properties of Maximum Likelihood Estimators and
(Generalized) Likelihood Ratio Statistics and, more generally, of Estimatiion
Equation solutions. As time permits, we will also something about
nonparametric (`rank') statistics which might be used with smaller or
moderate sized samples but which make most sense with larger samples.
Prerequisite: Stat 700 or equivalent. You should be comfortable
(after review) with joint densities, (multivariate, Jacobian)
changes of
variable, moment generating functions, and conditional expectation; and also
familiar with the definitions of
convergence in distribution, in probability,
and convergence with probability 1.
Texts: required Peter Bickel and Kjell Doksum, Mathematical
Statistics, vol.I, 2nd ed., Pearson Prentice Hall, 2007.
(recommended)
V. Rohatgi and A.K. Saleh, An Introduction to Probability and Statistics,
2nd ed., Wiley.
Approximate Stat 701 course coverage:
Bickel and Doksum: Chapter 4 Sections 4-5 and 7-9, along with
all of Chapters 5-6.
Rohatgi and Saleh: Sections 9.5-9.6, 10.2, Chapter 11 omitting
Sec. 11.4, and some of Ch.13 as time permits.
Course Grading: there will be assigned and graded homework due
approximately every 1.5 weeks (probably 7 in all). Homework
will count 45% toward
the course grade, Test(s) [in-class plus take-home] will count 35%, and final
exam will count 20%.
Click link here for syllabus, and here for the
Homework Assignments. Selected problem
solutions are given here.
NOTE that because of the snow closure Mar. 2, the due date for HW3 will
be extended to Friday March 6 at 5pm.
(You could fax or email or drop the HW off.)
Also note that there are some hints posted as of March 2, and
you should omit
the former part (ii) of Problem (IV).
Office hours: are Monday 2-3 and Thursday 1-2. I will
be available very often except on Tuesdays, but please send an e-mail
or arrange with me in class for an office appointment.
The topic coverage of the in-class Mid-term is as follows: TBA
There will be a second test, a Take-home, in the first week of May.
There will also be an in-class final.
(I). Handout on Prediction
intervals in (simple) linear regression in connection with
Prediction Intervals topic in Bickel & Doksum, Sec. 4.8.
(II). Handout on Chi-square
multinomial goodness of fit test.
(III). 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.
(IV). Handout on the 2x2
table asymptotics covered in class concerning different sampling
designs
and asymptotic distribution theory for the log odds ratio.
(V). Handout on Wald, Score
and LR statistics covered in class April 10 and 13, 2009.
Several typos have now been corrected (particularly in formulas (9)-(11)).