{"title":"A class of infinite number of unbiased estimators using weighted squared distance for two-deck randomized response model.","authors":"Daryan Naatjes, Stephen A Sedory, Sarjinder Singh","doi":"10.1080/02664763.2024.2399574","DOIUrl":null,"url":null,"abstract":"<p><p>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.</p>","PeriodicalId":15239,"journal":{"name":"Journal of Applied Statistics","volume":"52 4","pages":"868-893"},"PeriodicalIF":1.2000,"publicationDate":"2024-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11873971/pdf/","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied Statistics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/02664763.2024.2399574","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2025/1/1 0:00:00","PubModel":"eCollection","JCR":"Q2","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
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.
期刊介绍：
Journal of Applied Statistics provides a forum for communication between both applied statisticians and users of applied statistical techniques across a wide range of disciplines. These areas include business, computing, economics, ecology, education, management, medicine, operational research and sociology, but papers from other areas are also considered. The editorial policy is to publish rigorous but clear and accessible papers on applied techniques. Purely theoretical papers are avoided but those on theoretical developments which clearly demonstrate significant applied potential are welcomed. Each paper is submitted to at least two independent referees.
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