Statistics 5601 (Geyer, Fall 2006)

Midterm Exam

As announced, take home, due Wednesday, November 22, 2006. The due date has been extended to Wednesday, because they would probably not be graded until the following Monday anyway.

The test is this web page. To stand out from spam, put 5601 in the subject line. Students can also ask Prof. Chatterjee for clarifications.

Anyone wanting to hand in their exam early should hand it to Prof. Chatterjee or to one of the office staff (in Ford 313). Do not put it in anyone's mailbox or under anyone's door.

Queries

Query 1 about Question 2

Someone asked about why ltsreg doesn't give the same answers when run multiple times, even on the given data (never mind on random bootstrap data). Yes, that's what it does. The on-line help is clear as mud, but, as mentioned in class, exact minimization of the objective function is very hard so generally random search algorithms are used.

If you want an exact answer, you can add the argument nsamp = "exact" to the ltsreg function, but then it will take forever — I have no idea how long, I tried it, took a long shower, it was still running, so I killed it. Please don't experiment with this on rweb.stat.umn.edu. If you're running R at home you can try what you like.

If you want a better but non-exact answer, you can add the argument nsamp = 1e3 or some other number, the higher the number the better the answer (I think).

However, anyone who ignores all this and just uses the default behavior of ltsreg (no nsamp argument) won't be marked off for that. Don't mess with this unless you are (1) curious and (2) have the time.

(Added a bit later) if I use nsamp = 1e3 the bootstrap with nboot <- 250 takes 15 seconds on rweb.stat.umn.edu. If I use nsamp = 5e3 and nboot <- 250, it takes 58 seconds on rweb.stat.umn.edu. That's more than enough time for one job during a test. Anyone who wants to experiment with higher nsamp values, do it on your own computer, or, at least, after the test.

New! Homework 5 solutions posted (in the usual place with the usual user name and password).

New! What is LTS regression? The on-line help for the R ltsreg function says that LQS regression minimizes a specified quantile of the squared residuals, LMS regression minimizes the median (0.5 quantile) of the squared residuals, and LTS regression minimizes the sum of the quantile smallest squared residuals, the default being floor(n/2) + floor((p+1)/2), which is roughly 1 / 2 when n (number of cases) is much larger than p (number of regression coefficients). Thus LTS regression minimizes the sum of the squares of the smallest half of the residuals. The on-line help for the R ltsreg function says that LTS regression is more efficient than LQS (and its special case LMS), having different rates of convergence, n^{1 ⁄ 2} for LTS but n^{1 ⁄ 3} for LQS and LMS.

New! Homework 5, Problem 1 had additional wording added to make it clear that this estimate refers to mean(LakeHuron).

New! Homework 5 now posted.

New! At least temporarily, I have given up on a complete redesign of these web pages. The new Computer Examples link in the navigation section points to last semester's computer examples pages.

Tentative schedule to second midterm.

What	When
4th hw	Fri Nov 03
5th hw	Mon Nov 13
2nd exam	Fri–Mon Nov 17–20
Thanksgiving Holiday	Th–Fri Nov 23–24