The Annals of Mathematical Statistics

Sequential Probability Ratio Test for the Mean Value Function of a Gaussian Process

P. K. Bhattacharya and Robert P. Smith

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Abstract

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.

Article information

Source
Ann. Math. Statist., Volume 43, Number 6 (1972), 1861-1873.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177690857

Digital Object Identifier
doi:10.1214/aoms/1177690857

Mathematical Reviews number (MathSciNet)
MR395097

Zentralblatt MATH identifier
0263.62048

JSTOR
links.jstor.org

Citation

Bhattacharya, P. K.; Smith, Robert P. Sequential Probability Ratio Test for the Mean Value Function of a Gaussian Process. Ann. Math. Statist. 43 (1972), no. 6, 1861--1873. doi:10.1214/aoms/1177690857. https://projecteuclid.org/euclid.aoms/1177690857


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