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STA 7334: Assignments
AS = Asymptotic Statistics by A. W. van der Vaart
- Assignment 1 (Due Friday, Sep 24, by Noon)
- Do exercises 2.3, 2.4, and 2.5 of the course notes,
plus exercises 2.16 and 2.17 of AS.
In case the numbers change, here
is a copy of the
exercises at the time this assignment was made.
- Assignment 2 (Due Friday, Oct 1, by Noon)
- Exercises 2.12, 3.1, 3.4, and 3.8 of AS.
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.
- Assignment 3 (Due Friday, Oct 29, by Noon)
- Assignment 4 (Due Tuesday, Nov 16)
- Do exercises 5.1 and 5.2 of AS.
- Assignment 5 (Due by noon, Tuesday, Dec 14)
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 2.
- AS, Chapter 4
Exercises 1 and 3 are pretty simple and you should be able to
do them. Exercises 2, 4, and 5 are specifically about
exponential families, which we may return to later. Exercise
6 is more of an analysis question that bears on uniqueness of
the method of moments estimator.
- AS, Chapter 5
Exercises 4, 5, 6, 9, 10, 18 are routine examples and you
should be able to do them. Exercises 9, 17, and 19 are
standard counterexamples that everyone should know how to do.
You should do exercises 5.7 and 5.8 to make sure you
- AS, Chapter 12
Exercises 1, 6, 7, 9, 10, 11.