Asymptotic distributions for a class of generalized $L$-statistics
Copyright policy )Asymptotic distributions for a class of generalized $L$-statistics
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.
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)
- University of Sydney Australia
- Siberian Transport University Russian Federation
trimmed $U$-statistics, Asymptotic distribution theory in statistics, $U$-statistics, Mathematics - Statistics Theory, Statistics Theory (math.ST), \(U\)-statistics, trimmed \(U\)-statistics, Asymptotic properties of nonparametric inference, FOS: Mathematics, generalized $L$-statistics, weak convergence, generalized \(L\)-statistics
trimmed $U$-statistics, Asymptotic distribution theory in statistics, $U$-statistics, Mathematics - Statistics Theory, Statistics Theory (math.ST), \(U\)-statistics, trimmed \(U\)-statistics, Asymptotic properties of nonparametric inference, FOS: Mathematics, generalized $L$-statistics, weak convergence, generalized \(L\)-statistics
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).2 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!