Nonlinear principal components, II: Characterization of normal distributions

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Abstract

Nonlinear principal components are defined for normal random vectors. Their properties are investigated and interpreted in terms of the classical linear principal component analysis. A characterization theorem is proven. All these results are employed to give a unitary interpretation to several different issues concerning the Chernoff-Poincaré type inequalities and their applications to the characterization of normal distributions.

Original languageEnglish
Pages (from-to)652-660
Number of pages9
JournalJournal of Multivariate Analysis
Volume100
Issue number4
DOIs
Publication statusPublished - Apr 2009

Keywords

  • 47A75
  • 49R50
  • 60E05
  • 62H25
  • Chernoff inequality
  • Hermite polynomials
  • Nonlinear principal components
  • Normal distributions
  • primary
  • secondary

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