TY - JOUR

T1 - Logarithmic quantile estimation for rank statistics

AU - Denker, Manfred

AU - Tabacu, Lucia

PY - 2015/1/13

Y1 - 2015/1/13

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84911008557&partnerID=8YFLogxK

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U2 - 10.1080/15598608.2014.886312

DO - 10.1080/15598608.2014.886312

M3 - Article

AN - SCOPUS:84911008557

VL - 9

SP - 146

EP - 170

JO - Journal of Statistical Theory and Practice

JF - Journal of Statistical Theory and Practice

SN - 1559-8608

IS - 1

ER -