Local superefficiency of data-driven projection density estimators in continuous time

• Autores: D. Bosq, D. Blanke
• Localización: Sort: Statistics and Operations Research Transactions, ISSN 1696-2281, Vol. 28, Nº. 1, 2004, págs. 37-54
• Idioma: inglés
• Títulos paralelos:
  • Supereficiencia local de estimadores de densidad por proyección gobernados por los datos en tiempo continuo.
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• Resumen

  • We construct a data-driven projection density estimator for continuous time processes. This estimator reaches superoptimal rates over a class F0 of densities that is dense in the family of all possible densities, and a «reasonable» rate elsewhere. The class F0 may be chosen previously by the analyst. Results apply to Rd-valued processes and to N-valued processes. In the particular case where square-integrable local time does exist, it is shown that our estimator is strictly better than the local time estimator over F0.