A class of unbiased product-type estimators for the mean suitable for positive and negative correlation situations

Abstract

For estimating the population mean of a variable of interest, a class of unbiased estimators is derived by weighting the sample mean and two product-type estimators based on a transformation of an auxiliary variable and the jackknife technique. Numerous interesting estimators including those which may be used as a dual to the ratio estimator may be obtained from the proposed class. An exact expression for the variance is obtained, an optimum estimator in the class is found and the situations are identified under which estimators may be generated from the class which are better than the sample mean and the customary ratio and product estimators.