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

Claudio Durastanti; Nicola Turchi

doi:10.1080/10485252.2023.2208686

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arXiv · 2104.02427

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

Claudio Durastanti·Nicola Turchi

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Abstract

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.

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BibTeX RIS

Claudio Durastanti, Nicola Turchi. 2021-04-06. Nonparametric needlet estimation for partial derivatives of a probability density function on the $d$-torus. https://doi.org/10.1080/10485252.2023.2208686

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