Informatics and Applications
2015, Volume 9, Issue 2, pp 8892
NONPARAMETRIC ESTIMATION OF MULTIDIMENSIONAL DENSITY WITH THE USE OF WAVELET ESTIMATES OF UNIVARIATE PROJECTIONS
Abstract
The paper explores the computerized tomography method of inverting the Radon transformation for obtaining statistical estimates of multidimensional probability densities. This method utilizes nonlinear wavelet estimators of univariate projections to construct the multidimensional density estimate. Nonlinear wavelet estimators possess the ability to adapt to the local properties of the estimated density function and, therefore, are less sensitive to the singular points than linear estimators. Another important practical feature of the considered
method is its parallel structure, which allows a considerable speedup of constructing the estimates on the computers supporting parallel processing. It is also proved that under some regularity conditions, the uniform distance between the constructed estimate and the true multidimensional probability density converges to zero in the mean, and some estimates of the rate of this convergence are obtained.
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[+] About this article
Title
NONPARAMETRIC ESTIMATION OF MULTIDIMENSIONAL DENSITY WITH THE USE OF WAVELET ESTIMATES OF UNIVARIATE PROJECTIONS
Journal
Informatics and Applications
2015, Volume 9, Issue 2, pp 8892
Cover Date
20150230
DOI
10.14357/19922264150210
Print ISSN
19922264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
wavelets; multidimensional density; Radon transformation
Authors
O.V. Shestakov ,
Author Affiliations
Department of Mathematical Statistics, Faculty of Computational Mathematics and Cybernetics, M.V. Lomonosov Moscow State University, 152 Leninskiye Gory, GSP1, Moscow 119991, Russian Federation
Institute of Informatics Problems, Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, 442 Vavilov Str., Moscow 119333, Russian Federation
