Interval estimation for a binomial proportion: a bootstrap approach

Abstract

This paper discusses the classic but still current problem of interval estimation of a binomial proportion. Bootstrap methods are presented for constructing such confidence intervals in a routine, automatic way. Three confidence intervals for a binomial proportion are compared and studied by means of a simulation study, namely: the Wald confidence interval, the Agresti–Coull interval and the bootstrap-t interval. A new confidence interval, the Agresti–Coull interval with bootstrap critical values, is also introduced and its good behaviour related to the average coverage probability is established by means of simulations.

Keywords:

• Agresti and Coull confidence interval
• Binomial distribution
• Bootstrap
• Confidence intervals
• Coverage probability

Acknowledgements

The present paper is a result of the work that the authors did during their visiting in the department of Mathematics and Statistics, University of Cyprus in Cyprus, January–June 2006.