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Bahadur Representation for U-Quantiles of Dependent Data
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
Law of the Iterated Logarithm for U-Statistics of Weakly Dependent Observations
The law of the iterated logarithm for partial sums of weakly dependent
processes was intensively studied by Walter Philipp in the late 1960s and
1970s. In this paper, we aim to extend these results to nondegenerate
U-statistics of data that are strongly mixing or functionals of an absolutely
regular process.Comment: typos corrrecte
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