Asymptotic distributions of non-degenerate U-statistics on trimmed samples

Borovskikh, Yuri V.; Weber, N. C.

doi:10.1016/j.spl.2007.07.006

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“…Stigler [23] developed an asymptotic result for the trimmed mean without requiring continuity of the underlying distribution function associated with the observations. This result was extended to non-degenerate U -statistics based on trimmed samples in Borovskikh and Weber [4]. An alternative method for developing robust versions of U -statistics is to consider the statistic formed by trimming the kernel values, rather than the observations upon which the statistic is based.…”

Section: Introduction and Statement Of Resultsmentioning

confidence: 99%

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

Borovskikh¹,

Weber²

2010

Bernoulli

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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 Ustatistic summands. This approach leads to improved conditions for the asymptotic normality of these trimmed U -statistics.

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Section: Introduction and Statement Of Resultsmentioning

confidence: 99%