Monotonicity properties of the asymptotic relative efficiency between common correlation statistics in the bivariate normal model

Details Monotonicity properties of the asymptotic relative efficiency between common correlation statistics in the bivariate normal model Monotonicity properties of the asymptotic relative efficiency between common correlation statistics in the bivariate normal model

2009-07-31

arxiv.org/abs/0907.5448v1

Mathematics

Statistics Theory

Scientific paper

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.

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