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- W1567467353 abstract "Given data $X_1, dots, X_n$ and a kernel h with m arguments, Serfling introduced the class of generalized L-statistics (GL-statistics), which is defined by taking linear combinations of the ordered $h(X_{i_1}, dots, X_{i_m})$ where $(i_1, dots, i_m)$ ranges over all $n!/(n - m)!$ distinct m-tuples of $(1, dots, n)$. In this paper we derive a class of incomplete generalized L-statistics (IGL-statistics) by taking linear combinations of the ordered elements from a subset of ${h(X_{i_1}, dots, X_{i_m})}$ with size $N(n)$. A special case is the class of incomplete U-statistics, introduced by Blom. Under very general conditions, the IGL-statistic is asymptotically equivalent to the GL-statistic as soon as $N(n)/n to infty as n to infty$, which makes the IGL much more computationally feasible. We also discuss various ways of selecting the subset of ${h(X_{i_1}, dots, X_{i_m})}$. Several examples are discussed. In particular, some new estimates of the scale parameter in nonparametric regression are introduced. It is shown that these estimates are asymptotically equivalent to an IGL-statistic. Some extensions, for example, functionals other than L and multivariate kernels, are also addressed." @default.
- W1567467353 created "2016-06-24" @default.
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- W1567467353 date "1996-12-01" @default.
- W1567467353 modified "2023-09-26" @default.
- W1567467353 title "Incomplete generalized L-statistics" @default.
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- W1567467353 doi "https://doi.org/10.1214/aos/1032181173" @default.
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