This course is an introduction to mathematical statistics at the advanced calculus level. Prerequisites are advanced calculus (equivalent to MTH 435 or 437), linear algebra (MTH 215) and a course in probability (equivalent to MTH 451). No previous knowledge of statistics is assumed, though. The emphasis is on statistical theory rather than data analysis, but some applications (e.g. signal processing) will be featured.
Topics include: Review of probability (especially conditioning, multivariate normal distribution, distribution of transformations), statistical models, methods of estimation and comparison of methods, optimality theory for estimates, confidence intervals and hypothesis testing, introduction to large sample methods and optimal tests, regression and analysis of variance.
NOTE: This course has been revised this semester to include an introduction to modern methods such as EM algorithm and jackknife estimators. The textbook is new and the problem material has been revised.
Time: MW 4:30-5:45. The course will meet in Tyler Hall 106. .
For further information please contact
Instructor: L. Pakula, Tyler 201, X4-4519, pakula@math.uri.edu
Text: Keith Knight, Mathematical Statistics, Chapman and Hall/CRC
Chap. 2 Readings: pp. 16-27, 31-39,55-66,68-90,95-99 (You can omit Ex. 2.13, Thrm 2.8, and the section on projection matrices.)
Chap. 3 Readings: 113-125, 132-141, 146-149 (Proofs optional--we will do some of them in class.)
Chap. 4 Readings: 173-200, Omit Examples 4.20, 4.21, 4.24,4.27, 207-215 I will briefly discuss influence functions and jack-knife estimators in class.
Chap. 5 Readings: 237-240, 244-249, 254-257, 269-291. I will give more concise versions of some of this material in class.
Chap. 6 Readings: 307-326
Chap. 7 Readings: 339-349,354-376,381-388
Chap. 8 Readings: 403-411
ERRATA FOR PROBLEM SET 3 The statement of problem 3 is all messed up. It should read: If T is a complete sufficient statistic for theta then g(T) is ancillary if and only if g is a constant. (Sorry about that.)
The following Maple illustrates some ideas connected with empirical distributions and simulating r.v.s with given distributions, as well as some limitations of random number generators. If you have Maple on the machine you are using to read this, clicking on the link should open the worksheet in Maple.
Empirical d.f. and simulations
Here is a small Excel worksheet with which you can quickly find values
for normal, chi-square and t distributions -- better than tables.
If you have Excel on your computer
the sheet should open when you click on it. You can save it, of course,
but your system might tell you that it's written in an older version of
Excel (because it is!).
Statistical
distribution values
Here is a Maple worksheet that will allow you to experiment graphically
with some simple Bayesian priors.
Bayes
This Maple worksheets simulates the data and implements the EM
algorithm for the example we discussed in class.
EM
This worksheet simulates data and provides some graphics for the
example we discussed from the March 2003 Amer. Math. Monthly.
Darts
Here is the worksheet on power functions discussed in class. Power functions