University of Florida
Department of Statistics




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Brett Presnell
Associate Professor
225 Griffin-Floyd Hall
(352) 392 1941
FAX: (352) 392 5175

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MWF: 2:00pm–2:50pm

[FSF Associate Member]

STA 7334: Assignments

AS = Asymptotic Statistics by A. W. van der Vaart
CN = Course Notes

Assignment 1 (Due Friday, Oct 10)
  • CN 2.3, CN 2.4, CN 2.5, AN 2.12, AN 2.16 and AN 2.17. In case the numbers in the course notes change due to editing, here is a copy of the exercises with the numbering at the time this assignment was made.
Assignment 2 (Due Monday, Nov 17)
  • Exercises 11.5, 11.10, 12.1, 12.3, 12.7 of AS.
Assignment 3 (Due Wednesday, Dec 10)
  • Do exercises 5.1, 5.2, 5.7, and 5.13 of AS.

Additional Suggested Problems

AS, Chapter 2
You should be able to do all of the unassigned problems at the end of Chapter 2. Most of them are review problems for the probability course, and the majority are straightforward.
AS, Chapter 3
Again, you should be able to do most or all of the unassigned problems at the end of Chapter 3.

Note: the second part of AS 3.8, concerning the expectation of 1/|Xbar|, is false as stated for n = 1. It is true for n > 1, but is still somewhat difficult to prove. To make things easier, rather than assuming that the density f is bounded and strictly positive in a neighborhood of zero, assume that f is bounded away from zero in a neighborhood of zero, i.e., that there exists an eta > 0 and a delta > 0 such that f(x) > eta for all x with absolute value less than delta (this would be true for example if f was positive and continuous at zero). With these hypotheses E(1/|Xbar|) is infinite for all n >= 1.

AS, Chapter 5
Any of the unassigned exercises may be interesting and useful to attempt.
AS, Chapter 11
Exercises 7 and 8 may be interesting.
AS, Chapter 12
Exercises 6, 8, 10, and 11 may be interesting.

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