Nonnegative variance estimation in randomized response surveys

Abstract

Problems of estimation of the variances of linear homogeneous estimators of a finite population total of a variable of a sensitive nature are studied under randomized response (RR) Surveys. The nonnegativity property of the proposed estimator is also studied. It is shown that the nonnegetive variance estimator for RR surveys can always be obtained from the corresponding nonnegative estimator of the direct response (DR) surveys after simple modification. Sufficient Conditions of the nonnegativity of the variance estimators for a few well known sampling strategies are also presented here.