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