Kavya Pushadapu, Sarjinder Singh, Stephen A. Sedory
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Abstract
SummaryIn this paper, we begin by reviewing the optional randomised response technique estimator (ORRTE) developed by Chaudhuri and Mukerjee for estimating the proportion of a sensitive characteristic in a population. We show that their estimator is unbiased and has smaller variance than the Warner's estimator. Then we make an attempt at developing an optimised optional randomised response technique estimator (OORRTE). The proposed OORRTE is shown to be more efficient than the ORRTE. Findings from simulation studies are discussed and interpreted for various situations. Sample sizes for the Warner's estimator, the ORRTE and the OORRTE are computed based on power analysis introduced by Ulrich, Schroter, Striegel and Simon. Finally, we include an application to real data on COVID‐19 by considering it to be partially sensitive variable; that is, sensitive to some but not to others. The data used are included in the paper and the R‐codes used in the simulation study are documented in online material.
期刊介绍：
International Statistical Review is the flagship journal of the International Statistical Institute (ISI) and of its family of Associations. It publishes papers of broad and general interest in statistics and probability. The term Review is to be interpreted broadly. The types of papers that are suitable for publication include (but are not limited to) the following: reviews/surveys of significant developments in theory, methodology, statistical computing and graphics, statistical education, and application areas; tutorials on important topics; expository papers on emerging areas of research or application; papers describing new developments and/or challenges in relevant areas; papers addressing foundational issues; papers on the history of statistics and probability; white papers on topics of importance to the profession or society; and historical assessment of seminal papers in the field and their impact.
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