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

Manfred Denker, Madan L. Puri

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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 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 languageEnglish (US)
Pages (from-to)89-110
Number of pages22
JournalJournal of Statistical Planning and Inference
Volume32
Issue number1
DOIs
Publication statusPublished - Jul 1992

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All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

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