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

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:115

Article

Lei, LZ ; Wu, LM

关键词: large deviations;    kernel density estimator;    Donsker-Varadhan entropy;    uniformly ergodic Markov process;    Bahadur efficiency;   

DOI  :  10.1016/j.spa.2004.09.004

来源: Elsevier

【 摘 要 】

In this paper, we consider a uniformly ergodic Markov process (X-n)(ngreater than or equal to0) valued in a measurable subset E of R-d with the unique invariant measure mu(dx) =f(x)dx, where the ME density f is unknown. We establish the large deviation estimations for the nonparametric kernel density estimator f(n)* in L-1(R-d, dx) and for parallel tof(n)* - fparallel to(L1(Rd.dx)) and the asymptotic optimality f(n)* in the Bahadur sense. These generalize the known results in the i.i.d. case. (C) 2004 Elsevier B.V. All rights reserved.

【 授权许可】

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