Adaptive density estimation: A curse of support?

Adaptive estimation of convex and polytopal density support

We estimate the support of a uniform density, when it is assumed to be a convex polytope or, more generally, a convex body in R. In the polytopal case, we construct an estimator achieving a rate which does not depend on the dimension d, unlike the other estimators that have been proposed so far. For d ≥ 3, our estimator has a better risk than the previous ones, and it is nearly minimax, up to a...

Adaptive Dantzig density estimation

This paper deals with the problem of density estimation. We aim at building an estimate of an unknown density as a linear combination of functions of a dictionary. Inspired by Candès and Tao’s approach, we propose an l1-minimization under an adaptive Dantzig constraint coming from sharp concentration inequalities. This allows to consider a wide class of dictionaries. Under local or global coher...

Adaptive mixture density estimation

A~trac t -A recursive, nonparametric method is developed for performing density estimation derived from mixture models, kernel estimation and stochastic approximation. The asymptotic performance of the method, dubbed "adaptive mixtures" (Priebe and Marchette, Pattern Recognition 24, 1197-1209 (1991)) for its data-driven development of a mixture model approximation to the true density, is invest...

Location-Adaptive Density Estimation

Adaptive kernel density estimation

This insert describes the module akdensity. akdensity extends the official kdensity that estimates density functions by the kernel method. The extensions are of two types: akdensity allows the use of an “adaptive kernel” approach with varying, rather than fixed, bandwidths; and akdensity estimates pointwise variability bands around the estimated density functions.