Optimum stratification for allocation proportional to strata totals for scrambled response

The paper considers the problem of finding optimum strata boundaries to optimize the estimation of sensitive/stigmatized characters when sample sizes from different strata are allocated proportionally to strata totals of the auxiliary variable. Assuming the form of the regression of the estimation variable y on the auxiliary variable x as y = η ( x ) + e and the form of the conditional variance V ( y ∣ x ) , the rule for finding approximate optimum strata boundaries is proposed. The limiting expression of the variance of the estimator of mean in optimum stratification has also been obtained.