A0582
Title: Estimating the reciprocal of a binomial proportion
Authors: Jiajin Wei - Hong Kong Baptist University (Hong Kong) [presenting]
Ping He - Beijing Normal University - Hong Kong Baptist University United International College (China)
Tiejun Tong - Hong Kong Baptist University (Hong Kong)
Abstract: The binomial proportion is a classic parameter with many applications and has been extensively studied in the literature. By contrast, the reciprocal of the binomial or inverse binomial proportion is often overlooked, even though it also plays an important role in various fields. To estimate the inverse binomial proportion, the maximum likelihood method fails to yield a valid estimate when no successful event exists in the Bernoulli trials. To overcome this zero-event problem, several methods have been introduced in the previous literature. Yet to the best of our knowledge, there is little work on a theoretical comparison of the existing point estimators. Also, there is little work on the interval estimation for the inverse binomial proportion. To fill the gap, first, some commonly used point estimators for the inverse binomial proportion are reviewed, and then a new estimator is developed that aims to eliminate the estimation bias. Moreover, four different methods are applied to construct the confidence intervals (CIs), namely the Wald, score, arctangent and beta prime CIs, and further, their respective statistical properties are studied. Numerical studies are conducted to evaluate the finite sample performance of the proposed estimators, followed by a recent meta-analysis on the prevalence of heart failure among COVID-19 patients with mortality to demonstrate their usefulness in practice.
