Nonparametric needlet estimation for partial derivatives of a probability density function on the $d$-torus

Journal of Nonparametric Statistics (2023) This paper is concerned with the estimation of the partial derivatives of a probability density function of directional data on the $d$-dimensional torus within the local thresholding framework. The estimators here introduced are built by means of the toroi...

Full description

Saved in:
Bibliographic Details
Main Authors Durastanti, Claudio, Turchi, Nicola
Format Journal Article
LanguageEnglish
Published 06.04.2021
Subjects
Mathematics - Statistics Theory
Statistics - Theory
Online AccessGet full text

Cover

More Information
Summary:Journal of Nonparametric Statistics (2023) This paper is concerned with the estimation of the partial derivatives of a probability density function of directional data on the $d$-dimensional torus within the local thresholding framework. The estimators here introduced are built by means of the toroidal needlets, a class of wavelets characterized by excellent concentration properties in both the real and the harmonic domains. In particular, we discuss the convergence rates of the $L^p$-risks for these estimators, investigating on their minimax properties and proving their optimality over a scale of Besov spaces, here taken as nonparametric regularity function spaces.
DOI:10.48550/arxiv.2104.02427