Biological Statistics and Computational Genomics

Be solid, be open-minded


Quantile Regression 2013 Spring

Course Description

Lecture 1

Lecture 2

Lecture 3

Lecture 4 (No slides)

Lecture 5 (No slides)

Lecture 6

Lecture 7

Lecture 8

Lecture 9 (No slides)

Lecture 10 (No slides)

Lecture 11 (No slides)

Lecture 12

Lecture 13

Lecture 14

Reading Materials

Pollad (ET1991)

Kight (Annals 1998)

Kato (JMA 2009)

About MCMC

Chib and Greenberg (JASA 1992)

Casella and George (JASA 1992)

Dempster, Laird and Rubin (JRSSB 1977)

Tanner and Wong (JASA 1987)

Tierney (Annals 1994)

Markov Chain Monte Carlo Convergence Diagnostics: A Comparative Review

Optimal scaling for various Metropolis-Hastings algorithms

Weak convergence and optimal scaling of random walk Metropolis algorithms


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".

1. Analysis of treatment response data from eligibility designs (Chib and Jacobi 2008) 

2. Efficient Semiparametric Estimation of Quantile Treatment Effects (Firpo 2007)   

3. Baysian Spatial Quantile Regression (Dunson 2011)

4. Spatial Quantile Multiple Regression Using the Asymmetric Laplace Process (Lum and Gelfand 2012)

5. Noncrossing quantile regression curve estimation (Bondell, Reich and Wang 2010)

6. L1-norm quantile regression (Li and Zhu 2008)

7. Variable selection in quantile regression (Wu and Liu 2009)