Open Access
Translator Disclaimer
January, 1976 On the Asymptotic Normality of Kendall's Rank Correlation Statistic
Miloslav Jirina
Ann. Statist. 4(1): 214-215 (January, 1976). DOI: 10.1214/aos/1176343354

Abstract

Kendall's rank correlation statistic $T_n = \sum i > j \operatorname{sgn} (X_i - X_j)\cdot$ sgn $(Y_i - Y_j)$ is well known to be asymptotically normally distributed under the null hypothesis of independence as the sample size $n\rightarrow\infty$. In the note it is shown that this assertion can be obtained easily from the recurrence formula $p_n(t) = (1/n) \sum^n_{k =1}p_{n - 1}(t - 2k + n + 1)$ for the probability distribution $p_n$ of $T_n$ (see Kendall (1970), e.g.). This recurrence formula implies that $T_n$ has the same distribution as a sum of $(n - 1)$ well defined independent random variables to which the Lyapunov criterion applies.

Citation

Download Citation

Miloslav Jirina. "On the Asymptotic Normality of Kendall's Rank Correlation Statistic." Ann. Statist. 4 (1) 214 - 215, January, 1976. https://doi.org/10.1214/aos/1176343354

Information

Published: January, 1976
First available in Project Euclid: 12 April 2007

zbMATH: 0327.62039
MathSciNet: MR388614
Digital Object Identifier: 10.1214/aos/1176343354

Subjects:
Primary: 62E20

Keywords: asymptotic normality , Kendall rank correlation statistic , recurrence formula

Rights: Copyright © 1976 Institute of Mathematical Statistics

JOURNAL ARTICLE
2 PAGES


SHARE
Vol.4 • No. 1 • January, 1976
Back to Top