## Final Exam

Final exam is take-home, just like the other exams. It is due Tuesday December 19 by 4:30 when the Statistics Department office (Ford 313) closes.

The test is this web page.

The instructor (Geyer) will answer e-mail about the exam and put any answers of general interest here and on the exam page. I will also be in my office a lot during the exam. Just drop in with questions or phone before you come if you want to be sure I will be there.

It was noted that some old exam solutions were not readable. Now they all are

- Spring 2006
- Fall 2003
- Fall 2002
- Fall 2001 (questions are on a separate page)

All are password protected, the usual user name and password works.

## 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.

## Announcements

New! The last homework (number 7) has been graded and is in a box on the floor outside the instructor's office (Ford 356) if you want to pick it up.

Homework 7 solutions posted.

Two new handouts on theory page. One on subsampling bootstrap, one on smoothing.

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.

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 |

Info about installing and using R for those who wish to have R on their own computers.