A computational approach to the Kiefer-Weiss problem for sampling from a Bernoulli population

TL;DR

This paper introduces a computational method for solving the Kiefer-Weiss problem, specifically for Bernoulli populations, including algorithms implemented in R to construct optimal sampling plans and compare their performance with traditional tests.

Contribution

The paper develops and implements algorithms for optimal sampling plans for Bernoulli data, providing a computational approach to the Kiefer-Weiss problem and enabling performance evaluation.

Findings

Optimal tests outperform SPRT and fixed sample size tests in certain scenarios.

The R implementation facilitates practical application and comparison of sampling strategies.

Numerical results demonstrate the effectiveness of the proposed algorithms.

Abstract

We present a computational approach to solution of the Kiefer-Weiss problem. Algorithms for construction of the optimal sampling plans and evaluation of their performance are proposed. In the particular case of Bernoulli observations, the proposed algorithms are implemented in the form of R program code. Using the developed computer program, we numerically compare the optimal tests with the respective sequential probability ratio test (SPRT) and the fixed sample size test, for a wide range of hypothesized values and type I and type II errors. The results are compared with those of D.~Freeman and L.~Weiss (Journal of the American Statistical Association, 59(1964)). The R source code for the algorithms of construction of optimal sampling plans and evaluation of their characteristics is available at https://github.com/tosinabase/Kiefer-Weiss.