Open Access
Translator Disclaimer
May, 1978 Asymptotic Normality of Multivariate Linear Rank Statistics in the Non-I.I.D. Case
F. H. Ruymgaart, M. C. A. van Zuijlen
Ann. Statist. 6(3): 588-602 (May, 1978). DOI: 10.1214/aos/1176344203


Asymptotic normality is established for multivariate linear rank statistics of general type in the non-i.i.d. case covering null hypotheses as well as almost arbitrary alternatives. The functions generating the regression constants and the scores are allowed to have a finite number of discontinuities of the first kind, and to tend to infinity near 0 and 1. The proof is based on properties of empirical df's in the non-i.i.d. case and is patterned on the 1958 Chernoff-Savage method. As special cases e.g. rank statistics used for testing against regression and rank statistics for testing independence are included.


Download Citation

F. H. Ruymgaart. M. C. A. van Zuijlen. "Asymptotic Normality of Multivariate Linear Rank Statistics in the Non-I.I.D. Case." Ann. Statist. 6 (3) 588 - 602, May, 1978.


Published: May, 1978
First available in Project Euclid: 12 April 2007

zbMATH: 0408.62042
MathSciNet: MR464489
Digital Object Identifier: 10.1214/aos/1176344203

Primary: 62G10
Secondary: 62G17

Keywords: asymptotic normality , empirical df's , multivariate linear rank statistics , non-i.i.d. case

Rights: Copyright © 1978 Institute of Mathematical Statistics


Vol.6 • No. 3 • May, 1978
Back to Top