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

Liangzhen Lei and Liming Wu

Stochastic Processes and their Applications, 2005, vol. 115, issue 2, 275-298

Abstract: 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.

Keywords: Large; deviations; Kernel; density; estimator; Donsker-Varadhan; entropy; Uniformly; ergodic; Markov; process; Bahadur; efficiency (search for similar items in EconPapers)
Date: 2005
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Citations: View citations in EconPapers (1)

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