A robust unbiased dual to product estimator for population mean through modified maximum likelihood in simple random sampling

Abstract

In simple random sampling setting, the ratio estimator is more efficient than the mean of a simple random sampling without replacement (SRSWOR) if $ \\rho_{yx} > \\frac{1}{2}\\frac{{C_{x} }}{{C_{y} }} $, provided R > 0, which is usually the case. This shows that if auxiliary information is such that $ \\rho_{yx} < - \\frac{1}{2}\\frac{{C_{x} }}{{C_{y} }} $, then we cannot use the ratio method of estimation to improve the sample mean as an estimator of population mean. So there is need for another type of estimator which also makes use of information on auxiliary variable x. Product method of estimation is an attempt in this direction. Product-type estimators are widely used for estimating population mean when the correlation between study and auxiliary variables is negatively high. This paper is developed to the study of the estimation of the population mean using of unbiased dual to product estimator by incorporating robust modified maximum likelihood estimators (MMLE’s). Their properties have been obtained theoretically. For the support of the theoretical results, simulations studies under several super-population models have been made. We study the robustness properties of the modified estimators. We show that the utilization of MMLE’s in estimating finite population mean results to robust estimates, which is very gainful when we have non-normality or common data anomalies such as outliers.