Thresholding methods to estimate the copula density

TL;DR

This paper introduces adaptive wavelet-based thresholding methods for multivariate copula density estimation, demonstrating their effectiveness through theoretical analysis, simulations, and a financial data application.

Contribution

It presents novel adaptive thresholding procedures for copula density estimation that do not require prior regularity knowledge, with proven optimality properties.

Findings

Methods perform well under minimax and maxiset criteria.

Procedures can be distinguished in the maxiset sense.

Algorithm shows promising results in simulations and real data.

Abstract

This paper deals with the problem of the multivariate copula density estimation. Using wavelet methods we provide two shrinkage procedures based on thresholding rules for which the knowledge of the regularity of the copula density to be estimated is not necessary. These methods, said to be adaptive, are proved to perform very well when adopting the minimax and the maxiset approaches. Moreover we show that these procedures can be discriminated in the maxiset sense. We produce an estimation algorithm whose qualities are evaluated thanks some simulation. Last, we propose a real life application for financial data.