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Asymptotic Design of General Triangular Stopping Boundaries for Brownian Motion

Peng Huang
Lecture Notes-Monograph Series
Vol. 43, Crossing Boundaries: Statistical Essays in Honor of Jack Hall (2003), pp. 29-46
Stable URL: http://www.jstor.org/stable/4356261
Page Count: 18
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Asymptotic Design of General Triangular Stopping Boundaries for Brownian Motion
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Abstract

We consider triangular stopping boundaries for a Brownian motion with drift, with specified error probabilities at two given values for the drift. We consider the Kiefer-Weiss problem of finding boundaries which minimize the maximum expected stopping time asymptotically as the error probabilities tend to zero. A construction is given which minimizes the objective function through fourth order optimality. This extends earlier work for the simpler symmetric (equal error probabilities) case, where fifth order minimization was achieved.

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