handout

Large Sample Theory and Markov Chain Semester -I 02-03
http://www.isid.ac.in/~athreya/lsmc03

Instructor: Siva Athreya
Time: Tue, Thu-9:30-11:00am and Thu-2:00-3:00pm
Room: 24
Office: 213

References:

Approximation Theorems in Mathematical Statistics by R.J. Serfling.
Linear Statistical Inference and Its Applications by C.R. Rao.
Mathematical Methods of Statistics by H.Cramer.
A first course in stochastic processes by S. Karlin and H.M. Taylor.

E-Mail: My e-mail address is athreya@isid.ac.in.

WWW-page: I shall maintain a course home-page, at the following address:
http://www.isid.ac.in/~athreya/lsmc03 . The page should serve as a useful archive.

Tests: There shall be two exams in the semester.
Mid-term: September 19th, 2003
Final Exam: November 18th, 2003 **

** suggested date.

Homework: There will be regular homework assignments during the semester. A selection of which will be required to be turned in. You are encouraged to work together on solving the problems but write up your own individual solutions.

Quiz: There will be a short test on Tuesdays in the class. The test will have one question and will be essentially based out of the previous weeks homework.

Scoring: The Mid-term exam will be worth 35 %. Final exam is worth 40% of the score. Homework assignments and the Quizes will form the rest 25%.

Feedback: Please feel free to drop by my office to clear up difficulties. I would appreciate feedback from you as the course progresses. If there are suggestions/clarifications that you have then do let me know, either in class or in person or via email.

Dates Syllabus Covered

Aug 4-15 Review of various modes of convergence of random variables and

Central Limit Theorems. Cramer-Wold device. Scheffe's theorem.

Polya's theorem. Slutsky's theorem.

Aug 18-29 Variance stabilizing transformations Asymptotic distribution of order statistics.

Sep 1-23 Large sample properties of maximum likelihood estimates

and the method of scoring.

Sep 24-Oct 10 Pearson's chi-square statistic. Chi-square and likelihood ratio test statistics

for various hypotheses related to contingency tables.

Oct 13-Nov 7 Independence, Random walk, discrete time/discrete space

Markov chains - basic theory, examples including queueing/

birth-death chains/branching processes


Dates	Syllabus Covered


Aug 4-15	Review of various modes of convergence of random variables and
	Central Limit Theorems. Cramer-Wold device. Scheffe's theorem.
	Polya's theorem. Slutsky's theorem.


Aug 18-29	Variance stabilizing transformations Asymptotic distribution of order statistics.


Sep 1-23	Large sample properties of maximum likelihood estimates
	and the method of scoring.


Sep 24-Oct 10	Pearson's chi-square statistic. Chi-square and likelihood ratio test statistics
	for various hypotheses related to contingency tables.


Oct 13-Nov 7	Independence, Random walk, discrete time/discrete space
	Markov chains - basic theory, examples including queueing/
	birth-death chains/branching processes