Bahadur Representation for U-Quantiles of Dependent Data

Details Bahadur Representation for U-Quantiles of Dependent Data Bahadur Representation for U-Quantiles of Dependent Data

2010-04-15

arxiv.org/abs/1004.2581v3

J. Multivariate Anal. 102 (2011), no. 6, 1064-1079

Mathematics

Statistics Theory

Scientific paper

U-quantiles are applied in robust statistics, like the Hodges-Lehmann estimator of location for example. They have been analyzed in the case of independent random variables with the help of a generalized Bahadur representation. Our main aim is to extend these results to U-quantiles of strongly mixing random variables and functionals of absolutely regular sequences. We obtain the central limit theorem and the law of the iterated logarithm for U-quantiles as straightforward corollaries. Furthermore, we improve the existing result for sample quantiles of mixing data.

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