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A New Distance for Probability Measures Based on the Estimation of Level Sets

  • Alberto Muñoz
  • Gabriel Martos
  • Javier Arriero
  • Javier Gonzalez
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7553)

Abstract

In this paper we propose to consider Probability Measures (PM) as generalized functions belonging to some functional space endowed with an inner product. This approach allows to introduce a new family of distances for PMs. We propose a particular (non parametric) metric for PMs belonging to this class, based on the estimation of density level sets. Some real and simulated data sets are used for a first exploration of its performance.

Keywords

Probability Measure Functional Data Analysis Sparsity Measure Schwartz Distribution Hotelling Test 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Alberto Muñoz
    • 1
  • Gabriel Martos
    • 1
  • Javier Arriero
    • 1
  • Javier Gonzalez
    • 2
  1. 1.Department of StatisticsUniversity Carlos IIIMadridSpain
  2. 2.Johann Bernoulli Institute for Mathematics and Computer ScienceUniversity of GroningenThe Netherlands

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