Bahadur representation for U-Quantiles of dependent data
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Date
2010-04-26T10:17:39Z
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Abstract
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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Absolute regularity, Quantiles absolute regularity, Strong mixing, U-statistics