The Annals of Statistics

Asymptotic Normality of Multivariate Linear Rank Statistics in the Non-I.I.D. Case

F. H. Ruymgaart and M. C. A. van Zuijlen

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Abstract

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.

Article information

Source
Ann. Statist., Volume 6, Number 3 (1978), 588-602.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176344203

Digital Object Identifier
doi:10.1214/aos/1176344203

Mathematical Reviews number (MathSciNet)
MR464489

Zentralblatt MATH identifier
0408.62042

JSTOR
links.jstor.org

Subjects
Primary: 62G10: Hypothesis testing
Secondary: 62G17

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

Citation

Ruymgaart, F. H.; van Zuijlen, M. C. A. Asymptotic Normality of Multivariate Linear Rank Statistics in the Non-I.I.D. Case. Ann. Statist. 6 (1978), no. 3, 588--602. doi:10.1214/aos/1176344203. https://projecteuclid.org/euclid.aos/1176344203


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