The Annals of Statistics

On the asymptotic distribution of a general measure of monotone dependence

Donato Michele Cifarelli, Pier Luigi Conti, and Eugenio Regazzini

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In this paper the asymptotic normality of a class of statistics, including Gini's index of cograduation and Spearman's rank correlation coefficient, is proved. The asymptotic normality is stated under a large class of alternatives including the bivariate distributions corresponding to a condition of lack of association introduced in Section 3. The problems of testing the hypothesis of lack of association and of constructing confidence intervals for the population index of cograduation are also considered.

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Ann. Statist., Volume 24, Number 3 (1996), 1386-1399.

First available in Project Euclid: 20 September 2002

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Zentralblatt MATH identifier

Primary: 62H20: Measures of association (correlation, canonical correlation, etc.) 62G10: Hypothesis testing 62E20: Asymptotic distribution theory

Empirical processes functional limit theorem index of cograduation lack of association (= indifference) monotone dependence $U$-statistics


Cifarelli, Donato Michele; Conti, Pier Luigi; Regazzini, Eugenio. On the asymptotic distribution of a general measure of monotone dependence. Ann. Statist. 24 (1996), no. 3, 1386--1399. doi:10.1214/aos/1032526975.

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