# 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.