Robustness Evaluation in Sequential Testing of Composite Hypotheses
نویسندگان
چکیده
منابع مشابه
Robustness Evaluation in Sequential Testing of Composite Hypotheses
The problem of sequential testing of composite hypotheses is considered. Asymptotic expansions are constructed for the conditional error probabilities and expected sample sizes under “contamination” of the probability distribution of observations. To obtain these results a new approach based on approximation of the generalized likelihood ratio statistic by a specially constructed Markov chain i...
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Composite hypotheses are tested sequentially in many applications, especially in medicine and quality control (see Lai (2001)). Although some optimal properties of sequential tests are valid (see, for example, Malyutov et al. (2000)) in frames of hypothetical models, the observed data do not follow these models exactly, the hypothetical models are distorted (see Huber (2004) and Hampel et al. (...
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We study the stability of the classical optimal sequential probability ratio test based on independent identically distributed observations X1, X2, . . . when testing two simple hypotheses about their common density f : f = f0 versus f = f1. As a functional to be minimized, it is used a weighted sum of the average (under f0) sample number and the two types error probabilities. We prove that the...
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We study the problem of testing composite hypotheses versus composite alternatives, using a convex duality approach. In contrast to classical results obtained by Krafft & Witting [11], where sufficient optimality conditions are obtained via Lagrange duality, we obtain necessary and sufficient optimality conditions via Fenchel duality under some compactness assumptions. This approach also differ...
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We propose a new approach to sequential testing which is an adaptive (on-line) extension of the (off-line) framework developed in [1]. It relies upon testing of pairs of hypotheses in the case where each hypothesis states that the vector of parameters underlying the distribution of observations belongs to a convex set. The nearly optimal under appropriate conditions test is yielded by a solutio...
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ژورنال
عنوان ژورنال: Austrian Journal of Statistics
سال: 2016
ISSN: 1026-597X
DOI: 10.17713/ajs.v37i1.286