Adaptive Density Estimation on the Circle by Nearly-Tight Frames

2015/04/02 by Claudio Durastanti, Durastanti, Claudio
Mathematics · #62G07 #62G20 #62H11 #65T60 #FOS: Mathematics #Statistics Theory (math.ST) #math.ST #msc:62G07 #msc:62G20 #msc:62H11 #msc:65T60 #stat.TH

paper · pdf · doi:10.48550/arxiv.1504.00595

30 pages, 3 figures

arxiv created 2016/03/15 · arxiv updated 2016/03/16

Abstract

This work is concerned with the study of asymptotic properties of nonparametric density estimates in the framework of circular data. The estimation procedure here applied is based on wavelet thresholding methods: the wavelets used are the so-called Mexican needlets, which describe a nearly-tight frame on the circle. We study the asymptotic behaviour of the L²-risk function for these estimates, in particular its adaptivity, proving that its rate of convergence is nearly optimal.

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