2005/04/19 by Clementine Dalelane, Dalelane, Clementine
Decision Sciences · Engineering · #FOS: Mathematics #Fatigue and fracture mechanics #MSC 62C20 #Probabilistic and Robust Engineering Design #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.math/0504383
openalex publication_date 2005/04/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The L_2-minimax risk in Sobolev classes of densities with non-integer smoothness index is shown to have an analog form to that in integer Sobolev classes. To this end, the notion of Sobolev classes is generalized to fractional derivatives of order β∈\mathbb R+. A minimax kernel density estimator for such a classes is found. Although there exists no corresponding proof in the literature so far, the result of this article was used implicitly in numerous papers. A certain necessity that this gap had to be filled, can thus not be denied.