Optimal allocation in estimation of population mean in double sampling for stratification in presence of non-response and measurement error

Abstract

The study addresses the problem of minimum cost and precision in estimation of population mean in double sampling for stratification in presence of non-response and measurement error. Information on a single auxiliary variable is utilized to propose a ratio, exponential ratio-type and product-type estimators of population mean. Both the survey variable and auxiliary variable suffer from non-response and measurement error in the second phase sampling. The expression of biases and mean square errors of the proposed estimators are obtained upto the first order of approximation. The cost of the survey is studied theoretically. The optimum stratum sample sizes for the first phase sampling, second phase sampling and the optimum value of inverse sampling rate are obtained. Minimum cost function is attained when the value of lagrangian multiplier decreases leading to a minimum first phase and second phase stratum sample sizes.