On Accuracy Properties of Point Estimators for the Ratio of Binomial Proportions

Abstract

We continue our investigation on the ratio of binomial proportions started in Ngamkham et al. (2016) and Ngamkham (2018). Contrary to our previous research, where we were investigating interval estimations, here we concentrate on point estimation and its accuracy properties. A general problem of the point estimation for a ratio of two proportions according to data from two independent samples is considered. Each sample may be obtained in the framework of direct or inverse binomial sampling. Our goal is to show that the normal approximations (which are relatively simple) for estimates of the ratio are reliable for construction of point estimators. The main criterion of our judgment is the bias and mean squared error. It is shown by statistically modeled data that the scheme of inverse binomial sampling with planning of the size in the second sample is preferred (so-called special case of the direct-inverse sampling scheme). The main accuracy characteristics of estimators corresponding to all possible combinations of sampling schemes are investigated by the Monte Carlo method. Mean values and mean squared errors of point estimators are collected in tables, and some recommendations for an application of the estimators are presented.