Ratio Estimation of Finite Population Total in Stratified Random Sampling Under Non-response

Abstract

Estimation of population parameters has been an area of interest to many statisticians. Auxiliary variable that is highly correlated with the response variable can be used to improve efficiency of constructed estimators. Efficiency of constructed estimators is improved when more auxiliary variables are used in the survey problems. However, asymptotic properties of constructed estimators are usually interfered with by non-response in the study variable. Various corrective measures, such as imputation, partial deletion, resampling, weight adjustment and sub-sampling, have been suggested in literature to take care of the non-response. In this study, we have adopted the sub-sampling approach to construct a ratio estimator for finite population total in stratified random sampling under non-response. This has been done under both univariate and multivariate ratio estimations. In univariate case, we have considered separate and combined ratio estimations and regression forms of the constructed estimator. From the Percent Relative Efficiency (PRE) computations, we have observed that stratification improves performance of the constructed estimator by 10:26% compared to simple random sampling without replacement. Also, the sub-sampling method adopted improved efficiency of the constructed estimator by 0:44% when partial deletion is used. From multivariate unbiased ratio estimation, a two dimensional auxiliary random vector was constructed and it was observed that performance of the constructed multivariate ratio estimators depends on the choice of multivariate weights. This study has shown how an unbiased ratio estimator for finite population total is constructed in stratified random sampling. The study has also shown how the problem of non-response in sample surveys can be corrected using sub-sampling method. v