Super optimal rates for nonparametric density estimation via projection estimators

F. Comte and F. Merlevède

Stochastic Processes and their Applications, 2005, vol. 115, issue 5, 797-826

Abstract: In this paper, we study the problem of the nonparametric estimation of the marginal density f of a class of continuous time processes. To this aim, we use a projection estimator and deal with the integrated mean square risk. Under Castellana and Leadbetter's condition (Stoch. Proc. Appl. 21 (1986) 179), we show that our estimator reaches a parametric rate of convergence and coincides with the projection of the local time estimator. Discussions about the optimality of this condition are provided. We also deal with sampling schemes and the corresponding discretized processes.

Keywords: Castellana-Leadbetter's; condition; Continuous; time; projection; estimator; Markov; processes; Nonparametric; estimation; Local; time; Sampling (search for similar items in EconPapers)
Date: 2005
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Citations: View citations in EconPapers (2)

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