Author(s)

Diam Bâ¹, Cheikh Tidiane Seck², Gane Samb Lô^1,3

¹LERSTAD, Université Gaston Berger de Saint-Louis, Saint-Louis, Sénégal.
²LERSTAD, Université Alioune Diop, Bambey, Sénégal.
³LSTA, Université Pierre et Marie Curie, Paris, France.

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.

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

Bâ, D. , Seck, C. and Lô, G. (2015) Asymptotic Confidence Bands for Copulas Based on the Local Linear Kernel Estimator. Applied Mathematics, 6, 2077-2095. doi: 10.4236/am.2015.612183.