Large deviations of the kernel density estimator in L1(Rd) for reversible Markov processes

Lei, Liangzhen

Lei, Liangzhen

Bernoulli, Tome 12 (2006) no. 2, p. 65-83 / Harvested from Project Euclid

Résumé

We consider a reversible R^d-valued Markov process {X_i; 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 f_n^* in L¹(R^d,dx) and for {||f_n^*-f||}₁ are established. This generalizes the known results in the independent and identically distributed case. Furthermore, we show that f_n^* is asymptotically efficient in the Bahadur sense for estimating the unknown density f.

Publié le : 2006-02-14
Classification: Bahadur efficiency, kernel density estimator, large deviations, reversible Markov processes, uniformly integrable operators

@article{1141136649,
     author = {Lei, Liangzhen},
     title = {Large deviations of the kernel density estimator in L1(Rd) for reversible Markov processes},
     journal = {Bernoulli},
     volume = {12},
     number = {2},
     year = {2006},
     pages = { 65-83},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1141136649}
}

Lei, Liangzhen. Large deviations of the kernel density estimator in L1(Rd) for reversible Markov processes. Bernoulli, Tome 12 (2006) no. 2, pp.  65-83. http://gdmltest.u-ga.fr/item/1141136649/