Prem S. Puri Memorial Lecture

Wald's Equation for A Class of Denormalized U-statistics

Yuan Shih Chow
Professor of Statistics
Department of Mathematical Statistics, Columbia University

Start Date and Time: Thu, 18 Mar 1993, 4:30 PM

End Date and Time: Thu, 18 Mar 1993, 6:00 PM

Venue: MATH 175

Abstract:

For any integer k ≤ 1, define the de-normalized U-statistic Sk,n= ∑1 ≤ i1 < ... < ik ≤ n Xi1...Xik where {X, Xn, n ≥1} is an i.i.d. sequence with EX = 0. It is proved for k ≥ 2 that ESk,T = 0 whenever ElXlp < ∞, 1 < p ≤ 2 and T is a stopping time with E T(h-1)/(p-1)< ∞. This Wald-type equation is used to elicit information about the moments of Tk = inf{n ≥ k : Sk,n ≥ 0) and Wc = inf{n ≥ 2 : S1,n2 ≥ c ∑j=1nXj2}, c > 0. It is also noted that E|Sk, n/nk/p|p→ 0 if E|X|p < ∞, O < p < 2 provided EX = 0 when 1 ≤ p < 2.

Last Updated: Aug 31, 2017 11:37 AM

Purdue Department of Statistics, 250 N. University St, West Lafayette, IN 47907

Phone: (765) 494-6030, Fax: (765) 494-0558

© 2015 Purdue University | An equal access/equal opportunity university | Copyright Complaints

Trouble with this page? Disability-related accessibility issue? Please contact the College of Science Webmaster.