701 Topics outline  (Fall 2012)


T-test

Consistancy proof of MLE. (mostly for iid case)

Asymptotic distribution of MLE (normal distribution). Proof.

Wald test, Rao's score test, and Wilks likelihood ratio test.
The equivalence of the three tests.

Observed and expected Fisher information.

Nuisance parameter and parameter of interest. 
Profile out the nuisance parameter. (proof only for 1 parameter 
of interest and 1 nuisance parameter)
Nayman-Scott example.

Estimating equations (estimating functions).

Introduction to the empirical Bayes methodology. (examples. No detailed proof)

Introduction to the idea of Bootstrap method. (examples. No detailed proof)

Proof of CLT, Lyapunov condition, Lindeberg condition. for independent, 
not identically distributed rvs.

The Cramer-Wold device to prove the convergence of joint distributions. 
(via 1-dim rv)a (Multivariate CLT)

Dirichlet distribution.

The asymptotic distribution of sample median and sample quantiles.
The joint asymptotic distribution ofaseveral sample quantiles.
(no detailed proof)












Final Exam


This is a take home exam. But I strongly suggest you try to do
(at least half of the questions) under a limited time, to 
mimic the real test (to gain time managment skill)

2012:  Q5  Q6

2010:  Q3

2009:  Q6

2008:  Q7