Concomitants of Multivariate Order Statistics With Application to Judgment Poststratification

Abstract

We generalize the definition of a concomitant of an order statistic in the multivariate case, develop general expressions for its density, and establish related properties. We study the concomitant of a normal random vector in detail and discuss methods for calculating its moments. Furthermore, we apply the theory to develop new estimators of the mean from a judgment poststratified sample, where poststrata are formed by rank classes of auxiliary variables. Our estimators are shown to be more efficient than existing ones and robust against violations of the normality assumption. They are also well suited to applications requiring cost efficiency.