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In this paper, we consider the non-parametric estimation of the copula density under biased data. The contributions are both theoretical and practical. In the first part, we propose and develop a new wavelet-based methodology for this problem. In particular, a BlockShrink estimator is constructed, and we prove that it enjoys powerful mean integrated squared error properties over Besov balls. The second part is devoted to the applied aspect: we compare the performance of the wavelet-based estimator with that of a recently introduced kernel-based estimator through a detailed simulation study.

Wavelet block thresholding for copula density estimation under biased sampling