Modified product estimators of finite population mean in finite sampling

With respect to random sampling from finite population, when the correlation between the auxiliary and the main characteristics is negative, the product estimator is often used to estimate the population mean. The product estimator, however, would have a large mean-squared-error (MSE) if the coefficients of variations for these two characteristics were large and the absolute value of the correlation between them was small. In this paper, we propose a general family of modified product estimators, that include the product estimator as a special case. We provide a discussion on the reduction of the MSE by using the optimal modified product estimator that has the minimal MSE in the proposed family. In certain situations, these reductions of the MSE can be significant.