Hybrid estimators of population mean in presence of non-response and correlated measurement errors

Abstract

The present work deals with examining the effect of measurement errors on the design based statistical properties of the estimators of the population mean when the survey is encountered with some non-response. The technique of sub-sampling of non-respondents have been equipped with calibration techniques to handle the presence of non-response. Two kind of distance measures have been proposed and studied in detail to improve the calibration weights. The data on study as well as auxiliary variable has been assumed to be contaminated with correlated measurement errors. The specific properties of the estimators are derived under simple random sampling without replacement design. The proposed hybrid estimators are supported with numerical illustration incorporating simulation using specific population to show the applicability of proposed techniques practically. It is observed that the absolute relative bias of the estimators increase slightly with increase in error variance. Similarly, the precision of the estimators degrade with increase in error dispersion. Overall the proposed hybrid estimator with the chi-square type distance measure is observed to be remarkably efficient in comparison to the logarithmic type distance measure in presence of non-response and measurement errors.