Asymptotic confidence bands for copulas based on the local linear kernel estimator

TL;DR

This paper develops asymptotic confidence bands for copulas using a local linear kernel estimator, providing theoretical guarantees and demonstrating their effectiveness through simulations and an application to pseudo-panel data.

Contribution

It introduces asymptotic confidence bands for copulas based on a local linear kernel estimator, with proven uniform convergence and bias control under smoothness conditions.

Findings

Confidence bands are asymptotically valid under smoothness assumptions.

Bias of the estimator converges uniformly to zero at a specified rate.

Simulation study confirms the practical performance of the confidence bands.

Abstract

In this paper we establish asymptotic simultaneous confidence bands for copulas based on the local linear kernel estimator proposed by Chen and Huang [1]. For this, we prove under smoothness conditions on the copula function, 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 in a simulation study. An application based on pseudo-panel data is also provided for modeling dependence.