On Multivariate Ratio and Product Estimators

Abstract

Olkin (1958) proposed a multivariate generalization of the ratio estimator and Singh (1967) proposed a multivariate generalization of the product estimator of Murthy (1964). This note considers an alternative multivariate generalization of the ratio estimator for an arbitrary sampling design and shows that, to a first order of approximation, it has the same variance as Olkin's estimator. The multivariate ratio estimators are compared with the multivariate product and regression estimators with respect to variance and ease of computation. For the calculation of the multivariate ratio and product estimates an iterative procedure is suggested and demonstrated by working out an example.