On the correlations of the sign and ranks of observations in signal detection

In this paper, correlation coefficients between the sign and rank, sign and magnitude rank, and rank and magnitude rank of an observation in independent and identically distributed random vectors are obtained. It is shown that the sign, rank, and magnitude rank of an observation may or may not be uncorrelated depending on the distribution of the observation. Specifically, the correlation between the sign and magnitude rank and that between the rank and magnitude rank of an observation are zero for even symmetric distribution, and the correlation between the sign and rank of an observation is always nonnegative.