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

Abstract

We present a computational approach to the 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.

Keywords:

• Bernoulli trials
• hypothesis testing
• optimal sequential tests
• optimal stopping
• Kiefer-Weiss problem
• sequential analysis

SUBJECT CLASSIFICATIONS:

• 62L10
• 62L15
• 62F03
• 60G40
• 62M02

ACKNOWLEDGMENTS

The authors are very grateful to the anonymous referees and the editors for their substantial comments and suggestions, which contributed to making an early version of this work better.

DISCLOSURE

The authors have no conflicts of interest to report.

FUNDING

A. Novikov (Mexico) is grateful to SNI by CONACyT, Mexico, for partial support for his work. The work of A. Novikov (Russia) was partially supported by Russian Foundation for Basic Research Grant 19-29-01058. F. Farkhshatov thanks CONACyT, Mexico, for scholarship for his doctoral studies.