Almost sure central limit theorem for a nonstationary Gaussian sequence.
Zang, Qing-Pei (2010)
Journal of Inequalities and Applications [electronic only]
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Zang, Qing-Pei (2010)
Journal of Inequalities and Applications [electronic only]
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Panchenko, Dmitriy (2001)
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Zhongxue, Lü, Hongzheng, Xie (2002)
International Journal of Mathematics and Mathematical Sciences
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Papaschinopoulos, G., Schinas, C.J., Stefanidou, G. (2007)
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Alexander Rakhlin, Dmitry Panchenko, Sayan Mukherjee (2005)
ESAIM: Probability and Statistics
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In this paper we focus on the problem of estimating a bounded density using a finite combination of densities from a given class. We consider the Maximum Likelihood Estimator (MLE) and the greedy procedure described by Li and Barron (1999) under the additional assumption of boundedness of densities. We prove an bound on the estimation error which does not depend on the number of densities in the estimated combination. Under the boundedness assumption, this improves the bound of Li...
Panchenko, Dmitriy (2002)
Electronic Communications in Probability [electronic only]
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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...