Minimum variance stratification for scrambled response

Abstract

In this paper we have considered the problem of finding optimum strata boundaries (OSB) when the samples from different strata are selected with simple random sampling with replacement (SRSWR) and data are collected by scrambled randomized response technique on the sensitive variable. In the present paper a procedure which is applicable in more general situation is suggested for obtaining approximate optimum strata boundaries (AOSB). A limiting expression for the variance of the estimator of population mean, optimum number of strata, approximate expression for $[{\mathit{n}}_{\mathit{h}}]$ and expression for optimum cost allocated to L strata have also been suggested. The paper concludes with a numerical illustration.