2016/07/27 by Solesne Bourguin, Bourguin, Solesne, Claudio Durastanti +1 · 3 citations
Computer Science · Economics, Econometrics and Finance · Mathematics · #Bayesian Methods and Mixture Models #Stochastic processes and financial applications #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.1607.07981
In this paper, quantitative bounds in high-frequency central limit theorems\nare derived for Poisson based U-statistics of arbitrary degree built by means\nof wavelet coefficients over compact Riemannian manifolds. The wavelets\nconsidered here are the so-called needlets, characterized by strong\nconcentration properties and by an exact reconstruction formula. Furthermore,\nwe consider Poisson point processes over the manifold such that the density\nfunction associated to its control measure lives in a Besov space. The main\nfindings of this paper include new rates of convergence that depend strongly on\nthe degree of regularity of the control measure of the underlying Poisson point\nprocess, providing a refined understanding of the connection between regularity\nand speed of convergence in this framework.\n