Improved kernel estimation of copulas: weak convergence and goodness-of-fit testing

Abstract

We suggest modification of existing kernel estimators for a copula function in order to prevent corner bias problems when the second derivatives of the copula functions are unbounded. The theoretical contribution of the paper is a weak convergence result for the suggest estimators under conditions that are met for most copula families.

We also discuss the choice of bandwidth parameters, theoretically and practically, and illustrate the finite-sample behaviour of the estimators in a simulation study. The estimators are also applied to goodness-of-fit testing for copulas.

Keywords

• Improved
• kernel
• estimation
• copulas
• convergence
• goodness-of-fit
• testing