Adaptive smoothness of function estimation in the three classical problems of the non-parametrical statistic in the three classical problems of the non-parametrical statistic

TL;DR

This paper introduces an adaptive method for estimating the smoothness of functions in non-parametric statistics, applicable to regression, density, and spectral density estimation, using Hilbert space norms.

Contribution

It proposes a new adaptive approach for functional smoothness estimation across three classical non-parametric problems, enhancing flexibility and accuracy.

Findings

Effective in regression, density, and spectral density estimation

Improves estimation accuracy through adaptivity

Applicable in various non-parametric statistical contexts

Abstract

We offer in this short report the so-called adaptive functional smoothness estimation in the Hilbert space norm sense in the three classical problems of non-parametrical statistic: regression, density and spectral (density) function measurement (estimation).