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

Claudio Durastanti and Nicola Turchi

Journal of Nonparametric Statistics, 2023, vol. 35, issue 4, 733-772

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 $ L^p $ Lp-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.

Date: 2023
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DOI: 10.1080/10485252.2023.2208686

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