an:01768057
Zbl 0990.62042
Borkowf, Craig B.
Computing the nonnull asymptotic variance and the asymptotic relative efficiency of Spearman's rank correlation
EN
Comput. Stat. Data Anal. 39, No. 3, 271-286 (2002).
00086973
2002
j
62G20 62H20 65C60
asymptotic relative efficiency; asymptotic variance; empirical distribution functions; Fisher's transformation; simulations; Spearman's rank correlation
Summary: Over the past century, Spearman's rank correlation, \(\rho_{s}\), has become one of the most commonly used nonparametric statistics, yet much remains unknown about its finite and asymptotic behavior. This paper presents a method for computing the asymptotic variance of the point estimate, \(\hat\rho_{s}\), in terms of expectations of the joint and marginal distribution functions, for any underlying bivariate distribution that satisfies minimal regularity conditions. Also presented are numerical results for certain bivariate distributions of interest in order to demonstrate that distributions with similar values of Pearson's or Spearman's correlations can yield surprisingly different values for the asymptotic variance of \(\hat\rho_{s}\).
In particular, these results emphasize that one should not use certain standard procedures for hypothesis testing and confidence interval construction that assume bivariate normality without first checking this distributional assumption. Finally, these numerical results are used to compute the asymptotic relative efficiency of Spearman's rank correlation compared to Pearson's correlation.