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 AM  Vol.6 No.12 , November 2015
Asymptotic Confidence Bands for Copulas Based on the Local Linear Kernel Estimator
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.
Cite this paper: 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.
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