NDLI: Local Asymptotic Efficiency of a Sequential Probability Ratio Testfor d-Guarantee Discriminationof Composite Hypotheses

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Novikov, An. A. Volodin, I. N.
Copyright Year	1999
Abstract	A sequential Wald test for discrimination of two simple hypotheses $\theta=\theta_1$ and $\theta=\theta_2$ with boundaries A and B is applied to distinguish composite hypotheses $\theta<\theta_0$ and $\theta>\theta_0$, the parameters $\theta_1, \theta_2, A$, and B being chosen in such a way that d-posteriori probabilities of errors do not exceed the given restrictions $\beta_0$ and $\beta_1$. An asymptotic behavior of boundaries $A, B$ and the average observation time are studied when $\beta=\max\{\beta_0, \beta_1\}\to 0$. An asymptotic $(\beta\to 0)$ comparison is made of ${\bE}_{\theta}\nu$ with the least given number of observations necessary for discrimination of composite hypotheses with the same restrictions $\beta_0, \beta_1$ on d-posteriori probabilities of errors. It is shown that the minimum (in a neighborhood of the point $\theta=\theta_0$) gain of the average observation time makes up 25\%. Therefore, there are sequential tests within the bounds of a d-posteriori approach that give a gain in the size of observations for every value of a parameter tested.
Starting Page	269
Ending Page	281
Page Count	13
File Format	PDF
ISSN	0040585X
DOI	10.1137/S0040585X97976878
e-ISSN	10957219
Journal	Theory of Probability & Its Applications (TPRBAU)
Issue Number	2
Volume Number	43
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-25
Access Restriction	Subscribed
Subject Keyword	strict restrictions ond-risks sequential tests regular statistical experiments average size of observations discrimination of composite hypotheses Wiener process necessary size ofa sample asymptotic efficiency Bayesian paradigm d-posteriori approach d-guarantee
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Statistics, Probability and Uncertainty

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