Bernstein estimation for a copula derivative with application to conditional distribution and regression functionals

• Paul Janssen ^[1] ; Jan Swanepoel ^[2] ; Noël Veraverbeke ^[3]
  1. [1] University of Hasselt

     University of Hasselt

     Arrondissement Hasselt, Bélgica

     
  2. [2] North-West University

     North-West University

     Tlokwe City Council, Sudáfrica

     
  3. [3] Belgium North-West University

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• Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 25, Nº. 2, 2016, págs. 351-374
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • Bernstein estimators attracted considerable attention as smooth nonparametric estimators for distribution functions, densities, copulas and copula densities. The present paper adds a parallel result for the first-order derivative of a copula function. This result then leads to Bernstein estimators for a conditional distribution function and its important functionals such as the regression and quantile functions. Results of independent interest have been derived such as an almost sure oscillation behavior of the empirical copula process and a Bahadur-type almost sure asymptotic representation for the Bernstein estimator of a regression quantile function. Simulations demonstrate the good performance of the proposed estimators.