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Asymptotically optimal multistage hypothesis tests

Citation

Bartroff, Jay L. (2004) Asymptotically optimal multistage hypothesis tests. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd-05202004-133633

Abstract

This thesis investigates variable stage size multistage hypothesis testing in three different contexts, each building on the previous.

We first consider the problem of sampling a random process in stages until it crosses a predetermined boundary at the end of a stage -- first for Brownian motion and later for a sum of i.i.d. random variables. A multistage sampling procedure is derived and its properties are shown to be not only sufficient but also necessary for asymptotic optimality as the distance to the boundary goes to infinity.

Next we consider multistage testing of two simple hypotheses about the unknown parameter of an exponential family. Tests are derived, based on optimal multistage sampling procedures, and are shown to be asymptotically optimal.

Finally we consider multistage testing of two separated composite hypotheses about the unknown parameter of an exponential family. Tests are derived, based on optimal multistage tests of simple hypotheses, and are shown to be asymptotically optimal. Numerical simulations show marked improvement over group sequential sampling in both the simple and composite hypotheses contexts.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:asymptotic theory; multistage; sequential hypothesis testing
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Lorden, Gary A.
Thesis Committee:
  • Lorden, Gary A. (chair)
  • Wales, David B.
  • Candes, Emmanuel J.
  • Sherman, Robert P.
Defense Date:18 May 2004
Record Number:CaltechETD:etd-05202004-133633
Persistent URL:http://resolver.caltech.edu/CaltechETD:etd-05202004-133633
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1891
Collection:CaltechTHESIS
Deposited By: Imported from ETD-db
Deposited On:20 May 2004
Last Modified:26 Dec 2012 02:43

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