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ThesisItem Open Access SOME CONTRIBUTIONS IN THE THEORY OF CONSTRUCTION OF STRATA(UHF,NAUNI, 2016) THAKUR, ASHU; MAHAJAN, P.K.ABSTRACT The method of choosing the best boundaries that make strata internally homogeneous, given some sample allocation, is known as optimum stratification. To achieve this, the strata are constructed in such a way that the strata variances should be as small as possible for the characteristic under study. Present study considers the problem of finding optimum strata boundaries to optimize the estimation of sensitive/stigmatized characters when sample sizes from different strata are selected with simple random sampling with replacement (SRSWR) and probability proportional to size sampling with replacement (PPSWR) and the data are collected by scrambled randomized response technique on the sensitive study variable. Assuming the form of the regression of the estimation variable y on the auxiliary variable x as y = ƞ(x) + e and the form of the conditional variance V (Y/X), the minimal equations giving optimum strata boundaries by minimizing the variance of the estimator of the population mean have been obtained. Due to implicit nature of these equations, the approximate solutions to these minimal equations have been found to give approximate optimum strata boundaries (AOSB). The total four rules have been proposed to have AOSB i.e. for Neyman allocation with SRSWR, equal and proportional allocation in PPSWR and for ratio and regression method of estimation. Limiting expressions for the variance of the estimator of population mean have also been suggested. Numerical investigation into the relative efficiency of stratification under all considered allocations with respect to no stratification have also been made for three usually encountered distributions namely rectangular, right triangular and exponential.