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September, 1974 Asymptotic Normality of Nonparametric Tests for Independence
F. H. Ruymgaart
Ann. Statist. 2(5): 892-910 (September, 1974). DOI: 10.1214/aos/1176342812


Asymptotic normality of linear rank statistics for testing the hypothesis of independence is established both under fixed alternatives (or the null hypothesis) and under converging alternatives. The results of Ruymgaart, Shorack and van Zwet [14] are used to obtain a further weakening of the smoothness conditions on the score functions. In the present case the score functions are allowed to have a finite number of discontinuities of the first kind. The results of the present paper and of the paper [14] will be summarized in the author's thesis [13].


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F. H. Ruymgaart. "Asymptotic Normality of Nonparametric Tests for Independence." Ann. Statist. 2 (5) 892 - 910, September, 1974.


Published: September, 1974
First available in Project Euclid: 12 April 2007

zbMATH: 0303.62040
MathSciNet: MR386140
Digital Object Identifier: 10.1214/aos/1176342812

Primary: 62G10

Keywords: asymptotic normality , fixed alternatives , Rank statistics for independence , smoothness and growth of (limiting) score functions

Rights: Copyright © 1974 Institute of Mathematical Statistics


Vol.2 • No. 5 • September, 1974
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