Displaying similar documents to “The law of large numbers for U -statistics under absolute regularity.”

On strong laws for generalized L-statistics with dependent data

David Gilat, Roelof Helmers (1997)

Commentationes Mathematicae Universitatis Carolinae

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It is pointed out that a strong law of large numbers for L-statistics established by van Zwet (1980) for i.i.d. sequences, remains valid for stationary ergodic data. When the underlying process is weakly Bernoulli, the result extends even to generalized L-statistics considered in Helmers et al. (1988).

Dependent Lindeberg central limit theorem and some applications

Jean-Marc Bardet, Paul Doukhan, Gabriel Lang, Nicolas Ragache (2008)

ESAIM: Probability and Statistics

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In this paper, a very useful lemma (in two versions) is proved: it simplifies notably the essential step to establish a Lindeberg central limit theorem for dependent processes. Then, applying this lemma to weakly dependent processes introduced in Doukhan and Louhichi (1999), a new central limit theorem is obtained for sample mean or kernel density estimator. Moreover, by using the subsampling, extensions under weaker assumptions of these central limit theorems are provided. All the...