Generalized Classes of Regression-Cum-Ratio Estimators of Population Mean in Stratified Random Sampling

Abstract

In this paper, classes of separate and combined regression-cum-ratio estimators have been proposed for estimating the finite population mean in stratified random sampling. The expressions for biases and mean square errors (MSEs) of the proposed classes have been derived to the first order of approximation. It has also been verified that the proposed classes of estimators, at their optimum conditions, are equivalent to the separate regression estimator. The proposed classes of estimators have been compared with the other existing estimators using MSE criterion, and the conditions under which the proposed classes perform better have been obtained. Numerical illustrations are given in support of theoretical findings. Relevance of the work The estimation theory is relevant to various interdisciplinary areas of research including economics, clinical trials, population studies, engineering, agriculture, etc. Also, the problem of estimation of mean is of huge importance in research, for instance, the estimation of: average agricultural production, average life span of persons in a region, mean concentration of dissolved minerals in water, and much more. For the estimation of mean, several design-based approaches are being widely used, for instance, simple random sampling, stratified random sampling, two-phase sampling, etc. If the population under study is homogeneous, then the simple random sampling design is used at the estimation stage. However, in various practical situations, the research study is based on the heterogeneous population, and in that case the stratified random sampling procedure is preferable over the simple random sampling. Considering the above fact, an attempt has been made in this paper to develop the classes of generalized estimators for the mean of the variable under study using stratified random sampling.