Thresholding methods to estimate copula density

Abstract: This paper deals with the problem of multivariate copula density estimation. Using wavelet methods we provide two shrinkage procedures based on thresholding rules for which knowledge of the regularity of the copula density to be estimated is not necessary. These methods, said to be adaptive, have proved to be very effective when adopting the minimax and the maxiset approaches. Moreover we show that these procedures can be discriminated in the maxiset sense. We provide an estimation algorithm and evaluate its properties using simulation. Finally, we propose a real life application for financial data. AMS 2000 subject classifications: Primary 62G10, 62G20, 62G30. Keywords and phrases: copula density, wavelet method, thresholding rules, minimax theory, maxiset theory.

• Type: Journal
• Year: 2010
• Where: MA
• Authors: F. Autin, E. Le Pennec, K. Tribouley
• Keywords: Communications, Copula Density, Copula Density Estimation, MA 2010, Wavelet Method