Statistics 553
Asymptotic Tools
Fall 2004

General Information

General Information - Lecture Notes - Assignments - Textbook Errata

The FINAL EXAM with solutions is posted.
Time and Place MWF 8:00-8:50 in 219 Thomas
Instructor David Hunter
310 Thomas
Office hours: By arrangement (or just stop by).
Purpose This course will introduce students to some of the important statistical ideas of large-sample theory without requiring any mathematics beyond calculus and linear algebra. In particular, no measure theory is required. However, a basic understanding of statistics at the level of Statistics 513--514 will be assumed.
Intended Audience This course is required for all second-year PhD students in statistics. If you think you might be interested in taking it but you're not sure, please don't hesitate to come and talk to me.
Lecture notes Lectures will be based primarily on a set of lecture notes that I will print out and bring to class. They will also be posted on the web. I will be revising these notes throughout the semester, and because they are not quite in their final form I have listed a required textbook for this course. You might be able to get by without the required textbook, however -- I will leave this decision to each individual student.
Required Textbook E. L. Lehmann, Elements of Large-Sample Theory (Springer, 1999)
I like this book, especially for the level of this class. It is statistically rigorous without being overly mathematical and it contains many enlightening examples and exercises. It appears that this book is out of stock and may be hard to obtain. This won't be a serious problem, since the course notes will be available regardless.
Optional Textbook T. S. Ferguson, A Course in Large Sample Theory (Chapman and Hall, 1996)
This is a great book and I recommend it highly if you are interested in this subject. First of all, it's paperback so it's not as expensive as most statistics textbooks (it's roughly $60). Second, it has the very unusual yet enormously helpful feature that the exercises are all fully worked in the appendix (the best way to learn this stuff is to work problems, and with the solutions available to guide you when you get stuck, this book is ideal for self-study). Third, it is very concisely written, managing to pack a lot more information into the average page than the Lehmann book (partly this is because it is written almost entirely in the multivariate setting, so there is no separate treatment of the multivariate case). Fourth, it is divided into small, self-contained chunks, making it possible to sample different topics in almost any order you wish. You may wonder why, if it's such a great book, I don't use it as the main textbook for this course. The reason is that its mathematics is a bit more advanced than Lehmann's, and the whole point of this course is to present as much statistics as possible without relying on too deep a mathematical background.
Computing Computing will play a large role in the homework assignments. The software I'd recommend using is R or Splus, although I won't require any particular package or language. You can probably get by with Minitab if you're very comfortable with it, and packages such as Matlab or Mathematica or languages such as C or Fortran should be okay as well--however, before deciding to use one of these last 4, be sure you can obtain functions like the standard normal cdf and inverse cdf as well as random deviates from not just the uniform but all the common distributions as well. You will also need to be able to produce graphics such as histograms and plots of functions. If you're not currently familiar with R or Splus, I strongly encourage you to visit the R project web site at There, you can download R (for free!) and obtain documentation that will teach you the rudiments of both R and Splus (for the purposes of this class, R and Splus may be considered to be the same software package; R is a free version of Splus). Go to documentation, and download "An introduction to R," which will get you started if you skim it. Start with Chapter 2 if you want a very quick introduction to the language.
Grading There will be two midterms (15% each), a comprehensive final exam (20%), and weekly homework (50%). Most likely, the exams will be closed-book but you'll be allowed to bring a page or two of notes. This arrangement is similar to the rules for the qualifying review exam in January, which is comprised partly of questions on asymptotics. However, none of this is set in stone, so we can discuss other options if you prefer.
Integrity All Penn State and Eberly College of Science policies regarding academic integrity apply to this course. See for details.