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Journal of Statistical Theory and Practice

, Volume 9, Issue 1, pp 146–170 | Cite as

Logarithmic Quantile Estimation for Rank Statistics

  • Manfred Denker
  • Lucia Tabacu
Article

Abstract

We prove an almost sure weak limit theorem for simple linear rank statistics for samples with continuous distributions functions. As a corollary, the result extends to samples with ties and to the vector version of an almost sure (a.s.) central limit theorem for vectors of linear rank statistics. Moreover, we derive such a weak convergence result for some quadratic forms. These results are then applied to quantile estimation, and to hypothesis testing for nonparametric statistical designs, here demonstrated by the c-sample problem, where the samples may be dependent. In general, the method is known to be comparable to the bootstrap and other nonparametric methods (Thangavelu 2005; Fridline 2009), and we confirm this finding for the c-sample problem.

Keywords

Almost sure central limit theorem Rank statistics Logarithmic quantile estimation Kruskal-Wallis statistic 

AMS Subject Classification

62E20 62G20 

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Copyright information

© Grace Scientific Publishing 2015

Authors and Affiliations

  1. 1.Department of MathematicsPennsylvania State University, University ParkUSA
  2. 2.Department of StatisticsPennsylvania State University, University ParkUSA

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