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

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

2010-11-26

arxiv.org/abs/1011.5757v1

Bernoulli 2010, Vol. 16, No. 4, 1177-1190

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.3150/09-BEJ240 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statisti

Scientific paper

10.3150/09-BEJ240

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.

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