Adaptive Hausdorff estimation of density level sets

Adaptive Hausdorff Estimation of Density Level Sets

Hausdorff accurate estimation of density level sets is relevant in applications where a spatially uniform mode of convergence is desired to ensure that the estimated set is close to the target set at all points. The minimax optimal rate of error convergence for the Hausdorff metric is known to be (n/ logn) for level sets with Lipschitz boundaries, where the parameter α characterizes the regular...

Density Estimation with Adaptive Sparse Grids for Large Data Sets

Nonparametric density estimation is a fundamental problem of statistics and data mining. Even though kernel density estimation is the most widely used method, its performance highly depends on the choice of the kernel bandwidth, and it can become computationally expensive for large data sets. We present an adaptive sparse-grid-based density estimation method which discretizes the estimated dens...

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