Construction of Strata Boundaries under Ranked Set Sampling
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Date
2022-11
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Sher-e-Kashmir University of Agricultural Sciences and Technology of Jammu
Abstract
The principal reason for stratification in the design of sample surveys is to reduce the sample variance of the estimates, so as to gain a higher degree of relative precision. The problem of determining optimum strata boundaries (OSB) on the basis of study variable was pioneered by Dalenius (1950), who treated study variable itself as stratification variable and used an approach which provided exact solution. Researchers like Dalenius and Gurney (1951), Singh (1971), considered the problem of optimum stratification using auxiliary variable as stratification variable, since the probability density function of the study variable is in general unknown prior to study. In these studies simple random sampling was considered as method of selection of sampling units in individual strata. It is well known that ranked set sampling (RSS) introduced by McIntyre (1952) provides an increased precision as compared to simple random sampling. Thus, the RSS method if used for selection of sampling units in individual strata, the relative efficiency is expected to be increased. Therefore, the present investigation has been undertaken to deal with the problem of construction of strata when ranked set sampling is used. In this regard, various allocation procedures viz. proportional, optimum as well as equal allocations have been considered and accordingly the methods of construction of strata have been developed through minimization of variance under ranked set sampling.
The method of selecting the best boundaries that makes strata within them self-homogeneous as far as possible is known as optimum stratification. If the frequency distribution of the study variable is known, the stratification points could be obtained by cutting the range of the distribution. And, if unknown the points of stratification may be approximated on the basis of auxiliary variable. In the present study, theories have been developed for optimum stratification using one auxiliary variable as stratification variable. Minimal equations giving approximate optimum strata boundaries (AOSB) have been obtained for stratified ranked set sampling (SRSS) under different methods of allocations, by minimizing the variance of the sample estimates. For these cases, rule and rule , where the function takes different forms for different allocations, have been developed. Under the classical optimization technique the empirical studies on uniform, right triangular, exponential and normal distribution have been made which resulted gain in efficiency. On comparison of the efficiency, it has been observed that the proposed methods for SRSS under various methods of allocations performed better than unstratified RSS.
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Preferred for your workRather,K.U.I 2022.Construction of Strata Boundaries under Ranked Set Sampling.