## The Annals of Statistics

- Ann. Statist.
- Volume 11, Number 1 (1983), 306-316.

### An Efficient Approximate Solution to the Kiefer-Weiss Problem

#### Abstract

The problem is to decide on the basis of repeated independent observations whether $\theta_0$ or $\theta_1$ is the true value of the parameter $\theta$ of a Koopman-Darmois family of densities, where the error probabilities are at most $\alpha_0$ and $\alpha_1$. An explicit method is derived for determining a combination of one-sided SPRT's, known, as a 2-SPRT, which minimizes the maximum expected sample size to within $o((\log \alpha^{-1}_0)^{1/2})$ as $\alpha_0$ and $\alpha_1$ go to 0, subject to the condition that $0 < C_1 < \log \alpha_0/\log\alpha_1 < C_2 < \infty$ for fixed but arbitrary constants $C_1$ and $C_2$. For the case of testing the mean of an exponential density, extensive computer calculations comparing the proposed 2-SPRT with optimal procedures show that the 2-SPRT comes within 2% of minimizing the maximum expected sample size over a broad range of error probability and parameter values.

#### Article information

**Source**

Ann. Statist. Volume 11, Number 1 (1983), 306-316.

**Dates**

First available: 12 April 2007

**Permanent link to this document**

http://projecteuclid.org/euclid.aos/1176346081

**JSTOR**

links.jstor.org

**Digital Object Identifier**

doi:10.1214/aos/1176346081

**Mathematical Reviews number (MathSciNet)**

MR684888

**Zentralblatt MATH identifier**

0521.62065

**Subjects**

Primary: 62L10: Sequential analysis

Secondary: 62F03: Hypothesis testing

**Keywords**

Asymptotic efficiency sequential probability ratio test 2-SPRT

#### Citation

Huffman, Michael D. An Efficient Approximate Solution to the Kiefer-Weiss Problem. The Annals of Statistics 11 (1983), no. 1, 306--316. doi:10.1214/aos/1176346081. http://projecteuclid.org/euclid.aos/1176346081.