Locally most powerful sequential tests of a simple hypothesis vs. One-sided alternatives for independent observations

Let \(X_1,X_2,..., X_n,...\) be a stochastic process with independent values whose distribution \(P_\theta\) depends on an unknown parameter \(\theta\), \(\theta\in\Theta\), where \(\Theta\) is an open subset of the real line. The problem of testing \(H_0:\) \(\theta=\theta_0\) vs. a composite alter...

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Bibliographic Details
Published inarXiv.org
Main Authors Novikov, Andrey, Novikov, Petr
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 25.04.2010
Subjects
Parameters
Stochastic processes
Structural analysis
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Summary:Let \(X_1,X_2,..., X_n,...\) be a stochastic process with independent values whose distribution \(P_\theta\) depends on an unknown parameter \(\theta\), \(\theta\in\Theta\), where \(\Theta\) is an open subset of the real line. The problem of testing \(H_0:\) \(\theta=\theta_0\) vs. a composite alternative \(H_1:\) \(\theta>\theta_0\) is considered, where \(\theta_0\in\Theta\) is a fixed value of the parameter. The main objective of this work is the characterization of the structure of the locally most powerful (in the sense of Berk) sequential tests in this problem.
ISSN:2331-8422