A repeated significance test with applications to sequential detection in sensor networks

Authors:
Marco Guerriero;Vladimir Pozdnyakov;Joseph Glaz;Peter Willett
Affiliations:
Department of Electrical and Computer Engineering, University of Connecticut, Storrs, CT;Department of Statistics, University of Connecticut, Storrs, CT;Department of Statistics, University of Connecticut, Storrs, CT;Department of Electrical and Computer Engineering, University of Connecticut, Storrs, CT
Venue:
IEEE Transactions on Signal Processing
Year:
2010

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Abstract

In this paper we introduce a randomly truncated sequential hypothesis test. Using the framework of a repeated significance test (RST), we study a sequential test with truncation time based on a random stopping time. Using the functional central limit theorem (FCLT) for a sequence of statistics, we derive a general result that can be employed in developing a repeated significance test with random sample size. We present effective methods for evaluating accurate approximations for the probability of type I error and the power function. Numerical results are presented to evaluate the accuracy of these approximations.We apply the proposed test to a decentralized sequential detection problem in sensor networks (SNs) with communication constraints. Finally, a sequential detection problem with measurements at random times is investigated.