Inferences on the Correlation Coefficient in Bivariate Normal Populations from Ranked Set Samples

Abstract

Abstract Ranked set sampling was first used to obtain an improved estimate of a population mean. This technique is useful when a small random sample can be visually ordered easily and fairly accurately, but exact measurement of an observation is difficult or expensive. The sampling method is generalized and applied to estimation of the correlation coefficient ρ of a bivariate normal random vector (X, Y). The asymptotic variance of the maximum likelihood estimator of ρ based only on the extreme Y's and their concomitant X's is reduced over that from a random sample if the visual ordering is any better than random.