JSM 2003 Online Program

Abstract #300476

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Activity Number:	126
Type:	Contributed
Date/Time:	Monday, August 4, 2003 : 10:30 AM to 12:20 PM
Sponsor:	IMS
Abstract - #300476
Title:	Optimal Multistage Sampling in a Boundary-Crossing Problem
Author(s):	Jay Bartroff*+
Companies:	California Institute of Technology
Address:	Department of Mathematics, Pasadena, CA, 91125,
Keywords:	multistage ; Brownian motion ; asymptotic theory
Abstract:	Many problems in theoretical and applied statistics involve observing a random process until it crosses a predetermined boundary. We study a version of this classical problem in which Brownian motion with positive drift is sampled in stages until it crosses a given boundary A. The optimal stage-design strategy is defined to be that which minimizes a linear combination of the expectations of the stopping time and the number of stages used. We present a simple stage-design strategy and show it is asymptotically optimal for large A. Generalizations to sums of iid random variables and applications are discussed.

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