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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.