Homework 1: 1. Prove Theorem 2.3 in
the book 2. Show the formula on
Page 8 of Lecture 3. 3. Prove Kight's equality
4. Show the formula on Page 12 of Lecture 6
5. Show that the Jackknife variance estimator for mean works

Homework 2 :
1. Prove the second last formula on Page 182 of the book (Koenker).
2. Implement the Barrodale-Roberts algorithm for quantile regression
using R
3. Implement the Frisch–Newton interior algorithm for
quantile regression using R (optional)
4. Assume that X1,....Xn are sampled from a normal mixture distribution
p1N(mu1,sigma1^2)+(1-p1)N(mu2,sigma2^2). Derive an EM algorithm to
calculate the maximum likelihood estimator of the parameters.

Note: For problem 2 and 3, you should send
your code via email to me with a detailed instruction about how to run
your R code. The title of the email should be "Quantile regression HW2
code". Failure to do so may result in email loss and hence no score for
these two problems.

Reading
Material For Final

Email me about your
team members and which paper you are going to
report before May 2nd 2013

The due of the finla report is June 16 2013. The report should be
around 4-5 pages in pdf format. Please make sure the email for the
final report to me should be entitled with "Quantile Regression Final
Report".