Showing papers by "Miguel A. Arcones published in 1995"
TL;DR: The local law of the iterated logarithm for Gaussian processes indexed by arbitrary index sets is discussed, in particular for self-similarGaussian processes.
Abstract: We present some optimal conditions for the compact law of the iterated logarithm of a sequence of jointly Gaussian processes in different situations. We also discuss the local law of the iterated logarithm for Gaussian processes indexed by arbitrary index sets, in particular for self-similar Gaussian processes. We apply these results to obtain the law of the iterated logarithm for compositions of Gaussian processes.
72 citations
TL;DR: In this article, a Bernstein-type inequality for non-degenerated U-statistics is presented for the case of U-processes indexed by a uniformly bounded VC subgraph class of functions.
70 citations
TL;DR: The law of the iterated logarithm for U -processes indexed by canonical Vapnik-Cervonenkis classes of functions with square integrable envelope was proved in this paper.
60 citations
TL;DR: In this article, the central limit theorem for U-statistics whose underlying sequence of random variables satisfies an absolute regularity condition under optimal assumptions is proved for any class of U-Statistics.
24 citations
TL;DR: The asymptotic normality of the trimmed mean, obtained by deleting the data which is further away from a parameter of location [theta]n, is proved.
12 citations
TL;DR: The order of the Kolmogorov-Smirnov distance for the bootstrap of quantiles is investigated in this article, where it is shown that the order depends on the local variance of the first term of the Hoeffding decomposition at the quantile.
Abstract: The order of the Kolmogorov-Smirnov distance for the bootstrap of $U$-quantiles is considered. We observe that the order of the bootstrap of $U$-quantiles depends on the order of the local variance of the first term of the Hoeffding decomposition at the $U$-quantile. This order can be smaller than the order of the bootstrap of quantiles: $U$-quantiles can be smoother than quantiles.
7 citations
TL;DR: The compact law of the iterated logarithm for empirical processes whose underlying sequence satisfies a β-mixing condition is considered in this paper, where the authors show a compact law for VC subgraph classes of functions.
Abstract: The compact law of the iterated logarithm for empirical processes whose underlying sequence satisfies a β-mixing condition is considered. In particular, we show a compact law of the iterated logarithm for VC subgraph classes of functions, for classes of functions which satisfy the bracketing condition in Doukhanet al.
(6) and for some classes of smooth functions.
4 citations