STA 7334: Assignments

AS = Asymptotic Statistics by A. W. van der Vaart

Assignment 1 (Due Thurs, Aug 31)

AS 2.7, 2.19

Assignment 2 (Due Thurs, Sep 7)

Prove that conditions (ii) and (iv) of the Portmanteau theorem are equivalent.

Assignment 3 (Due Thurs, Sept 14)

Do this problem plus AS 2.16, 2.17

Assignment 4 (Due Thurs, Sept 28)

Do this problem plus AS 2.12

Assignment 5 (Due Thurs, Oct 5)

Do this problem plus AS 3.8
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 quite 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 6 (Due Thursday, Oct 26)

AS: 4.1, 4.2.

Assignment 7 (Due Tuesday, Nov 21)

AS: 5.1, 5.2, 5.3, 5.11.

Additional Problems

AS, Chapter 2

You should be able to do all the problems at the end of Chapter 2. Most of them are straightforward. Some of the more interesting ones are 2.5, 2.7, 2.8, 2.9, 2.10, 2.11, 2.12, 2.15, 2.16, 2.17, 2.18, 2.19, 2.20, 2.21, 2.22, 2.23