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Deheuvels, P. (1979) La fonction de dépendence empirique et ses propriétés. Un test non paramétrique. d’indépendance. Bulletin Royal Belge de l’Académie des Sciences, 65, 274-292.

has been cited by the following article:

• TITLE: Asymptotic Confidence Bands for Copulas Based on the Local Linear Kernel Estimator

  AUTHORS: Diam Bâ, Cheikh Tidiane Seck, Gane Samb Lô

  KEYWORDS: Copula Function, Kernel Estimation, Local Linear Estimator, Uniform in Bandwidth Consistency, Simultaneous Confidence Bands

  JOURNAL NAME: Applied Mathematics, Vol.6 No.12, November 25, 2015

  ABSTRACT: In this paper, we establish asymptotically optimal simultaneous confidence bands for the copula function based on the local linear kernel estimator proposed by Chen and Huang [1]. For this, we prove under smoothness conditions on the derivatives of the copula a uniform in bandwidth law of the iterated logarithm for the maximal deviation of this estimator from its expectation. We also show that the bias term converges uniformly to zero with a precise rate. The performance of these bands is illustrated by a simulation study. An application based on pseudo-panel data is also provided for modeling the dependence structure of Senegalese households’ expense data in 2001 and 2006.