NDLI: Locally Most Powerful Sequential Tests of a Simple Hypothesis vs. One-Sided Alternatives for Independent Observations

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Novikov, An. A. Novikov, P. A.
Copyright Year	2012
Abstract	Let a stochastic process with independent values $X_1,X_2,\dots, X_n,\dots$ be observed and let its distribution $P_\theta$ depend on an unknown parameter $\theta$. In this paper we consider the problem of testing a simple hypothesis $H_0:\theta=\theta_0$ vs. a composite alternative $H_1:\theta>\theta_0$, where $\theta_0\in\Theta$ is a fixed value of the parameter. In the first part of this work we present conditions for differentiability (at $\theta_0$) of the power function of any sequential test and obtain some inequalities of informational type relating the average sample number with the type-I probability error to the derivative of the power function of sequential tests. In the second part of the work we characterize the structure of locally most powerful (in the sense of Berk [Ann. Statist., 3 (1975), pp. 373--381]) sequential tests in this problem (maximizing derivative of a power function under given constraints on the type-I probability error and the average sample number).
Starting Page	420
Ending Page	442
Page Count	23
File Format	PDF
ISSN	0040585X
DOI	10.1137/S0040585X97985492
e-ISSN	10957419
Journal	Theory of Probability and its Applications (TPRBAU)
Issue Number	3
Volume Number	56
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2012-01-01
Access Restriction	Subscribed
Subject Keyword	locally most powerful test optimal sequential decision sequential analysis one-sided alternative statistical hypothesis testing sequential test
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Statistics, Probability and Uncertainty

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