Optimum stratification with ratio and regression methods of estimation

Summary The paper considers the problem of optimum stratification on an auxiliary variablex when the information on the auxiliary variablex is also used to estimate the population mean using ratio or regression methods of estimation. Assuming the form of the regression of the estimation variabley on the auxiliary variablex as also the form of the conditional variance function V(y/x), the problem of determining optimum strata boundaries (OSB) is shown to be a particular case of optimum stratification on the auxiliary variable for stratified simple random sampling estimate. A numerical investigation has also been made to study the amount of gain in efficiency that can be brough about by stratifying the population.