Large deviations of kernel density estimator in L1(Rd) for uniformly ergodic Markov processes

In this paper, we consider a uniformly ergodic Markov process (Xn)n[greater-or-equal, slanted]0 valued in a measurable subset E of Rd with the unique invariant measure , where the density f is unknown. We establish the large deviation estimations for the nonparametric kernel density estimator in L1(Rd,dx) and for , and the asymptotic optimality in the Bahadur sense. These generalize the known results in the i.i.d. case.

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Year of publication:	2005
Authors:	Lei, Liangzhen ; Wu, Liming
Published in:	Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 115.2005, 2, p. 275-298
Publisher:	Elsevier
Keywords:	Large deviations Kernel density estimator Donsker-Varadhan entropy Uniformly ergodic Markov process Bahadur efficiency

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10008875075