Copula density estimation | Erwan LE PENNEC

joint work with F. Autin and K. Tribouley

The copula of a random vector describes the dependence between its coordinates, independently of their marginal distributions. Wavelet thresholding being a versatile nonparametric technique, we applied it to the estimation of the copula density.

Thresholding on rank-based pseudo-observations

With F. Autin and K. Tribouley, we proposed wavelet thresholding estimators of the copula density. As the marginal distributions are unknown, these estimators are computed from rank-based pseudo-observations, which are not independent, and this is the main technical difficulty compared with direct density estimation (J. Multivariate Anal. 2010).

Adaptivity and numerical study

We proved that these estimators are adaptive and nearly minimax optimal over Besov balls, and we compared several thresholding methods in numerical experiments on simulated and real datasets.

Publications

2010 (1)

Journal articles

Thresholding methods to estimate the copula density. F. Autin, E. Le Pennec, K. Tribouley. J. Multivariate Anal., 101(1):200–222, 2010. PDF DOI arXiv HAL

BibTeX

@article{autin10:_thres,
  author = {Autin, F. and Le Pennec, E. and Tribouley, K.},
  title = {Thresholding methods to estimate the copula density},
  journal = {J. Multivariate Anal.},
  number = {1},
  volume = {101},
  pages = {200--222},
  year = {2010},
  doi = {10.1016/j.jmva.2009.07.009},
  eprint = {0802.2424},
  archiveprefix = {arXiv}
}

2008 (1)

Technical reports

Thresholding methods to estimate the copula density. F. Autin, E. Le Pennec, K. Tribouley. LPMA, Extended version arXiv:0802.2424, 2008. PDF arXiv

BibTeX

@techreport{autin08:_thres,
  author = {Autin, F. and Le Pennec, E. and Tribouley, K.},
  title = {Thresholding methods to estimate the copula density},
  institution = {LPMA},
  note = {Extended version arXiv:0802.2424},
  year = {2008},
  eprint = {0802.2424},
  archiveprefix = {arXiv}
}