A family of minimax rates for density estimators in continuous time

A family of minimax rates for density estimators in continuous time

In continuous time, rates of convergence of density estimators fluctuate with the nature of observed sample paths. In this paper, we give a family of rates reached by the kernel estimator and we show that these rates are minimax. Finally, we study applications of these results for specific classes o...

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Veröffentlicht in:Stochastic analysis and applications 2000, Vol.18 (6), p.871-900
Hauptverfasser: Blanke, D., Bosq, D.
Format: Artikel
Sprache:eng
Schlagworte:
62M
Continuous Time Process
Estimator
Exact sciences and technology
Inference from stochastic processes
time series analysis
Intermediate Rate
Kernel Density
Mathematics
Minimax Rate
Multivariate analysis
Nonparametric Estimation
Nonparametric inference
Probability and statistics
Sciences and techniques of general use
Statistics
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Beschreibung
Zusammenfassung:In continuous time, rates of convergence of density estimators fluctuate with the nature of observed sample paths. In this paper, we give a family of rates reached by the kernel estimator and we show that these rates are minimax. Finally, we study applications of these results for specific classes of processes including the Gaussian ones
ISSN:0736-2994
1532-9356
DOI:10.1080/07362990008809702