Optimum stratification for scrambled response with ratio and regression methods of estimation

Abstract

The paper considers the problem of optimum stratification when the information on the auxiliary variable x is used to estimate the population mean ${\mathit{y}}^{-}$ of the sensitive study variable y using ratio and regression methods of estimation and the data are collected by scrambled randomized response technique on the sensitive character. The paper proposes cum. $\sqrt[3]{{\mathit{p}}_4\mathrm{(}\mathit{x}\mathrm{)}}$ rule for finding approximate optimum strata boundaries (AOSB).