Approximately optimum stratification for ratio and regression methods of estimation

This work considers the problem of optimum stratification for two study variables Yj(j=1,2) when samples from different strata are collected by simple random sampling with a replacement scheme and the information on the auxiliary variable is used to estimate the population mean using the ratio and regression method of estimation. A cumulative cube root rule for determination of optimum strata boundaries for the ratio and regression method of estimation under compromise allocation has been proposed. A limiting expression for the trace of the variance–covariance matrix has also been suggested. The work concludes with a numerical illustration.