A class of infinite number of unbiased estimators using weighted squared distance for two-deck randomized response model.

Abstract

We develop a collection of unbiased estimators for the proportion of a population bearing a sensitive characteristic using a randomized response technique with two decks of cards for any choice of weights. The efficiency of the estimator depends on the weights, and we demonstrate how to find an optimal choice. The coefficients of skewness and kurtosis are introduced. We support our findings with a simulation study that models a real survey dataset. We suggest that a careful choice of such weights can also lead to all estimates of proportion lying between [0, 1]. In addition, we illustrate the use of the estimators in a recent study that estimates the proportion of students, 18 years and over, who had returned to the campus and tested positive for COVID-19.