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December, 1972 Sequential Probability Ratio Test for the Mean Value Function of a Gaussian Process
P. K. Bhattacharya, Robert P. Smith
Ann. Math. Statist. 43(6): 1861-1873 (December, 1972). DOI: 10.1214/aoms/1177690857


Sequential probability ratio tests are defined for testing a simple hypothesis against a simple alternative for the mean value function of a real Gaussian process with known covariance kernel. Exact formulas are obtained for the error probabilities and the OC function using the fact that the $\log$ likelihood ratio process is a Gaussian process with independent increments and have continuous sample paths. An identity of a familiar nature holds for the expected value of the $\log$ likelihood ratio process at a random stopping time. In certain situations this identity yields an exact formula for the ASN function. Two examples are given. The analysis employs the theory of reproducing kernel Hilbert spaces.


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P. K. Bhattacharya. Robert P. Smith. "Sequential Probability Ratio Test for the Mean Value Function of a Gaussian Process." Ann. Math. Statist. 43 (6) 1861 - 1873, December, 1972.


Published: December, 1972
First available in Project Euclid: 27 April 2007

zbMATH: 0263.62048
MathSciNet: MR395097
Digital Object Identifier: 10.1214/aoms/1177690857

Rights: Copyright © 1972 Institute of Mathematical Statistics

Vol.43 • No. 6 • December, 1972
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