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Superresolution Rates in Prokhorov Metric

Published online by Cambridge University Press:  20 November 2018

P. Doukhan  and
F. Gamboa
P. Doukhan
Affiliation:
Modélisation stochastique et Statistiques: U.R.A. C.N.R.S. D0743 Orsay Bât 425 F-91405 Orsay Cedex, e-mail: doukhan@stats.matups.fr
F. Gamboa
Affiliation:
Modélisation stochastique et Statistiques: U.R.A. C.N.R.S D0743 Orsay Bât 425 F-91405 Orsay Cedex and Université Paris-Nord Institut Galilée F-93430 Villetaneuse, e-mail: gamboa@stats.matups.fr
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Abstract

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Consider the problem of recovering a probability measure supported by a compact subset U of ℝm when the available measurements concern only some of its Ф-moments (Ф being an ℝk valued continuous function on U). When the true Ф-moment c lies on the boundary of the convex hull of Ф(U), generalizing the results of [10], we construct a small set Rα,δ(∊) such that any probability measure μ satisfying is almost concentrated on Rα,δ(∊). When Ф is a pointwise T-system (extension of T-systems), the study of the set Rα,δ(∊) leads to the evaluation of the Prokhorov radius of the set .

Keywords

52A4043A0762A99Generalized momentssuperresolutionT-systemsProkhorov metric
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 48 , Issue 2 , 01 April 1996 , pp. 316 - 329
Copyright
Copyright © Canadian Mathematical Society 1996

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