Asymptotic normality of two sample linear rank statistics under U-statistic structure

Manfred Denker; Madan L. Puri

doi:10.1016/0378-3758(92)90154-K

Asymptotic normality of two sample linear rank statistics under U-statistic structure

Manfred Denker, Madan L. Puri

Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

We prove the asymptotic normality of the two sample linear rank statistic when the independent samples arise from U-statistics with kernels of varying degree. The proof uses variance estimates of the empirical process of U-statistic structure and the continuity theorem in Denker and Rösler (1985b). This method also applies to other rank statistics. We give a sharp upper bound for the asymptotic efficacy of these statistics when the kernels are order preserving.

Original language	English (US)
Pages (from-to)	89-110
Number of pages	22
Journal	Journal of Statistical Planning and Inference
Volume	32
Issue number	1
DOIs	https://doi.org/10.1016/0378-3758(92)90154-K
State	Published - Jul 1992

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty
Applied Mathematics

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abstract = "We prove the asymptotic normality of the two sample linear rank statistic when the independent samples arise from U-statistics with kernels of varying degree. The proof uses variance estimates of the empirical process of U-statistic structure and the continuity theorem in Denker and R{\"o}sler (1985b). This method also applies to other rank statistics. We give a sharp upper bound for the asymptotic efficacy of these statistics when the kernels are order preserving.",

author = "Manfred Denker and Puri, \{Madan L.\}",

note = "Funding Information: Correspondenze to; Prof. Madan L. Puri, Dept. of Mathematics, Bloomington, IN 47405, USA. * Research supported by the Office of Naval Research, Grant Copyright: Copyright 2014 Elsevier B.V., All rights reserved.",

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AU - Puri, Madan L.

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PY - 1992/7

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N2 - We prove the asymptotic normality of the two sample linear rank statistic when the independent samples arise from U-statistics with kernels of varying degree. The proof uses variance estimates of the empirical process of U-statistic structure and the continuity theorem in Denker and Rösler (1985b). This method also applies to other rank statistics. We give a sharp upper bound for the asymptotic efficacy of these statistics when the kernels are order preserving.

AB - We prove the asymptotic normality of the two sample linear rank statistic when the independent samples arise from U-statistics with kernels of varying degree. The proof uses variance estimates of the empirical process of U-statistic structure and the continuity theorem in Denker and Rösler (1985b). This method also applies to other rank statistics. We give a sharp upper bound for the asymptotic efficacy of these statistics when the kernels are order preserving.

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ER -

Asymptotic normality of two sample linear rank statistics under U-statistic structure

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