Asymptotic distributions for a class of generalized $L$-statistics

Yuri V. Borovskikh; N. C. Weber

doi:10.3150/09-BEJ240

Asymptotic distributions for a class of generalized $L$-statistics

Statistics Theory 2010-11-29 v1 Statistics Theory

Authors: Yuri V. Borovskikh , N. C. Weber

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Abstract

We adapt the techniques in Stigler [Ann. Statist. 1 (1973) 472--477] to obtain a new, general asymptotic result for trimmed $U$ -statistics via the generalized $L$ -statistic representation introduced by Serfling [Ann. Statist. 12 (1984) 76--86]. Unlike existing results, we do not require continuity of an associated distribution at the truncation points. Our results are quite general and are expressed in terms of the quantile function associated with the distribution of the $U$ -statistic summands. This approach leads to improved conditions for the asymptotic normality of these trimmed $U$ -statistics.

Keywords

generalized L-statistics trimmed U-statistics asymptotic distributions quantile function asymptotic normality

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@article{arxiv.1011.5757,
  title  = {Asymptotic distributions for a class of generalized $L$-statistics},
  author = {Yuri V. Borovskikh and N. C. Weber},
  journal= {arXiv preprint arXiv:1011.5757},
  year   = {2010}
}

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Published in at http://dx.doi.org/10.3150/09-BEJ240 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

Asymptotic distributions for a class of generalized $L$-statistics

Abstract

Keywords

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