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Statistics & Risk Modeling

with Applications in Finance and Insurance

Editor-in-Chief: Stelzer, Robert

4 Issues per year


Cite Score 2016: 0.33

SCImago Journal Rank (SJR) 2016: 0.346
Source Normalized Impact per Paper (SNIP) 2016: 0.167

Mathematical Citation Quotient (MCQ) 2016: 0.32

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Volume 26, Issue 1 (Mar 2008)

Issues

A kernel-based classifier on a Riemannian manifold

Jean-Michel Loubes / Bruno Pelletier
  • 1 Université Montpellier II, CC 051, Institut de Mathématiques et de Modélisation de Mo, Montellier Cedex 5, Frankreich
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Published Online: 2009-09-25 | DOI: https://doi.org/10.1524/stnd.2008.0911

Abstract

Let X be a random variable taking values in a compact Riemannian manifold without boundary, and let Y be a discrete random variable valued in {0;1} which represents a classification label. We introduce a kernel rule for classification on the manifold based on n independent copies of (X,Y). Under mild assumptions on the bandwidth sequence, it is shown that this kernel rule is consistent in the sense that its probability of error converges to the Bayes risk with probability one.

Keywords: classification; kernel rule; Bayes risk; consistency

About the article

* Correspondence address: Université de Toulouse 3, Institut de Mathématiques, Route de Narbonne, bat 1R2, bureau 115, Equipe de Statistique et Probabilités UMR 5219, 31062 Toulouse, Frankreich,


Published Online: 2009-09-25

Published in Print: 2008-03-01


Citation Information: Statistics & Decisions International mathematical journal for stochastic methods and models, ISSN (Print) 0721-2631, DOI: https://doi.org/10.1524/stnd.2008.0911.

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