A comparison of some confidence intervals for a binomial proportion based on a shrinkage estimator

Abstract

Confidence intervals are valuable tools in statistical practice for estimating binomial proportions, with the most well-known being the Wald and Clopper-Pearson intervals. However, it is known that these intervals perform poorly in terms of coverage probability and expected mean length, leading to the proposal of alternative intervals in the literature, although these may also have deficiencies. In this work, we investigate the performance of several of these confidence intervals using the parametric family p ^ c = X + c n + 2 c {\widehat{p}}_{c}=\frac{X+c}{n+2c} with c ≥ 0 c\ge 0 to estimate the parameter p p . Rather than using the confidence intervals approach, this analysis is done from the hypothesis tests approach. Our primary goal with this work is to identify values of c c that result in better-performing tests and to establish an optimal procedure.

The Testing Procedure for the Overall Lifetime Performance Index of Rayleigh Products in Multiple Production Lines Based on the Progressive Type I Interval Censored Sample

“…For the confidence intervals for binomial distribution in Equation ( 16), Jäntschi [20] proposed three alternative confidence interval calculation methods and algorithms to improve the nominal coverage probabilities compared to the Wald asymptotic interval method. Félix et al [21] improved the performance of several confidence intervals, including the Wald, Wilson score, and arcsine confidence intervals, by using the parametric family pc = X+c n+2c with c ≥ 0 to estimate the parameter p, where X is the number of successes out of n trials. Rather than using the confidence intervals approach, their analysis was conducted based on the hypothesis test approach.…”