  Pearson's is the most common correlation statistic, used mainly in parametric
settings. Most common among nonparametric correlation statistics are Spearman's
and Kendall's. We show that for bivariate normal i.i.d. samples the pairwise
asymptotic relative efficiency between these three statistics depends
monotonically on the population correlation coefficient. This monotonicity is a
corollary to a stronger result. The proofs rely on the use of l'Hospital-type
rules for monotonicity patterns.
