An efficient variant of the product and ratio estimators

Abstract  This article presents a variant of the usual ratio and product methods of estimation, with the intention 10 improve their efficiency. The first order large sample approximations to the bias and the mean square error of the proposed estimator are obtained and compared with those of the well-known methods (simple expansion, ratio, product, difference and linear regression methods). For a special case, the accuracy of the first order approximation (terms up to the order n-¹ ) is examined by including terms upto the order n^-2 . With suitable choice of a design parameter, the proposed estimator turns out to be superior to the three methods mentioned first. The relation to the other two methods is examined; if the design parameter can be chosen near to the optimal value, the proposed method is seen to be approximately as efficient as the linear regression estimator. Finally some extensions are indicated.