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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
- 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
- AS, Chapter 11
Exercises 7 and 8 may be interesting.
- AS, Chapter 12
Exercises 6, 8, 10, and 11 may be interesting.