Adaptive density estimation: a curse of support? ✩
By Patricia Reynaud-Bouret, Vincent Rivoirard, Christine Tuleau-Malot. 2009
62 citations recorded by the source corpus.
This paper deals with the classical problem of density estimation on the real line. Most of the existing papers devoted to minimax properties assume that the support of the underlying density is bounded and known. But this assumption may be very diffi cult to handle in practice. In this work, we show that, exactl y as a curse of dimensionality exists when the data lie in R d , there exists a curse of support as well when the support of the density is infinite. As for the dimensional ity problem where the rates of convergence deteriorate when the dimension grows, the minimax rates of convergence may deteriorate as well when the support becomes infinite. This problem is not purely theo retical since the simulations show that the support-dependent methods are really affected in practice by the size of the density support, or by the weight of the density tail. We propose a method based on a biorthogonal wavelet thresholding rule that is adaptive with respect to the nature of the support and the regularity of the signal, but that is also robust in practice to this curse of support. The threshold, that is pro posed here, is very accurately calibrated so that the gap between optimal theoretical and practical tuning parameters is almost filled.
Subfields: Applied Mathematics, Computational Mechanics, Computer Vision and Pattern Recognition
View Paper: https://www.semanticscholar.org/paper/b1ce824fa26b6675ce8a644d002fcb68e1ceee0b
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
In Computational Mechanics
In Computer Vision and Pattern Recognition
Citations in the corpus
- Posterior concentration rates for infinite dimensional exponential families (2012, background): “[16] and in the Bayesian context where least favorable priors for such spaces are built (see Johnstone [12] or Rivoirard [17]).”