Translator Disclaimer
February 2006 Large deviations of the kernel density estimator in L1(Rd) for reversible Markov processes
Liangzhen Lei
Author Affiliations +
Bernoulli 12(1): 65-83 (February 2006).

Abstract

We consider a reversible Rd-valued Markov process {Xi; i≥0} with the unique invariant measure μ(dx)=f(x)dx, where the density f is unknown. The large-deviation principles for the nonparametric kernel density estimator fn* in L1(Rd,dx) and for {||fn*-f||}1 are established. This generalizes the known results in the independent and identically distributed case. Furthermore, we show that fn* is asymptotically efficient in the Bahadur sense for estimating the unknown density f.

Citation

Download Citation

Liangzhen Lei. "Large deviations of the kernel density estimator in L1(Rd) for reversible Markov processes." Bernoulli 12 (1) 65 - 83, February 2006.

Information

Published: February 2006
First available in Project Euclid: 28 February 2006

MathSciNet: MR2202321

Rights: Copyright © 2006 Bernoulli Society for Mathematical Statistics and Probability

JOURNAL ARTICLE
19 PAGES


SHARE
Vol.12 • No. 1 • February 2006
Back to Top