Monotonicity properties of the asymptotic relative efficiency between common correlation statistics in the bivariate normal model
Statistics Theory
2009-08-03 v1 Probability
Computation
Statistics Theory
Abstract
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.
Keywords
Cite
@article{arxiv.0907.5448,
title = {Monotonicity properties of the asymptotic relative efficiency between common correlation statistics in the bivariate normal model},
author = {Raymond Molzon and Iosif Pinelis},
journal= {arXiv preprint arXiv:0907.5448},
year = {2009}
}