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 characterised by excellent concentration properties in both the real and the harmonic domains. In particular, we discuss the convergence rates of the (Formula presented.) -risks for these estimators, investigating their minimax properties and proving their optimality over a scale of Besov spaces, here taken as nonparametric regularity function spaces.

Durastanti, C., Turchi, N. (2023). Nonparametric needlet estimation for partial derivatives of a probability density function on the d-torus. JOURNAL OF NONPARAMETRIC STATISTICS, 35(4), 733-772 [10.1080/10485252.2023.2208686].

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

Turchi, N
2023

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 characterised by excellent concentration properties in both the real and the harmonic domains. In particular, we discuss the convergence rates of the (Formula presented.) -risks for these estimators, investigating their minimax properties and proving their optimality over a scale of Besov spaces, here taken as nonparametric regularity function spaces.
Articolo in rivista - Articolo scientifico
adaptivity; directional data; Local thresholding; needlets; nonparametric density estimation;
English
5-mag-2023
2023
35
4
733
772
none
Durastanti, C., Turchi, N. (2023). Nonparametric needlet estimation for partial derivatives of a probability density function on the d-torus. JOURNAL OF NONPARAMETRIC STATISTICS, 35(4), 733-772 [10.1080/10485252.2023.2208686].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/401474
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