Evading the curse of dimensionality in nonparametric density estimation with simplified vine copulas

Thomas Nagler, Claudia Czado

Research output: Contribution to journalArticlepeer-review

102 Scopus citations

Abstract

Practical applications of nonparametric density estimators in more than three dimensions suffer a great deal from the well-known curse of dimensionality: convergence slows down as dimension increases. We show that one can evade the curse of dimensionality by assuming a simplified vine copula model for the dependence between variables. We formulate a general nonparametric estimator for such a model and show under high-level assumptions that the speed of convergence is independent of dimension. We further discuss a particular implementation for which we validate the high-level assumptions and establish asymptotic normality. Simulation experiments illustrate a large gain in finite sample performance when the simplifying assumption is at least approximately true. But even when it is severely violated, the vine copula based approach proves advantageous as soon as more than a few variables are involved. Lastly, we give an application of the estimator to a classification problem from astrophysics.

Original languageEnglish
Pages (from-to)69-89
Number of pages21
JournalJournal of Multivariate Analysis
Volume151
DOIs
StatePublished - 1 Oct 2016

Keywords

  • Asymptotic
  • Classification
  • Copula
  • Dependence
  • Kernel density
  • Vine

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