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

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.

40 pages, 4 figures, 4 tables

References in corpus (3)

• Asymptotics for spherical needlets
• Subsampling needlet coefficients on the sphere
• Exploring wind direction and SO2 concentration by circular-linear density estimation