## The Annals of Mathematical Statistics

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

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

P. K. Bhattacharya and Robert P. Smith

#### 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