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Super optimal rates for nonparametric density estimation via projection estimators. (English) Zbl 1065.62057

Summary: We study the problem of 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 J. V. Castellana and M. R. Leadbetter’s condition [Stochastic Processes Appl. 21, 179–193 (1986; Zbl 0588.62156)], 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.

MSC:

62G07 Density estimation
62M09 Non-Markovian processes: estimation
62G20 Asymptotic properties of nonparametric inference

Citations:

Zbl 0588.62156
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References:

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