2005/04/19 by Clementine Dalelane, Dalelane, Clementine
Computer Science · Mathematics · #62G20 #FOS: Mathematics #Image and Signal Denoising Methods #MSC: 62G07 #Mathematical Approximation and Integration #Statistical Methods and Inference #Statistics Theory (math.ST) #math.ST #msc:62G07 #msc:62G20 #stat.TH
paper · pdf · doi:10.48550/arxiv.math/0504382
arxiv created 2005/04/19 · openalex publication_date 2005/04/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In one-dimensional density estimation on i.i.d. observations we suggest an adaptive cross-validation technique for the selection of a kernel estimator. This estimator is both asymptotic MISE-efficient with respect to the monotone oracle, and sharp minimax-adaptive over the whole scale of Sobolev spaces with smoothness index greater than 1/2. The proof of the central concentration inequality avoids "chaining" and relies on an additive decomposition of the empirical processes involved.