Density estimation through convex combinations of densities: Approximation and estimation bounds

Assaf J. Zeevi*, Ronny Meir

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We consider the problem of estimating a density function from a sequence of N independent and identically distributed observations X(i) taking value in X c R(d). The estimation procedure constructs a convex mixture of 'basis' densities and estimates the parameters using the maximum likelihood method. Viewing the error as a combination of two terms, the approximation error measuring the adequacy of the model, and the estimation error resulting from the finiteness of the sample size, we derive upper bounds to the expected total error, thus obtaining bounds for the rate of convergence. These results then allow us to derive explicit expressions relating the sample complexity and model complexity.

Original languageEnglish
Pages (from-to)99-109
Number of pages11
JournalNeural Networks
Volume10
Issue number1
DOIs
StatePublished - Jan 1997
Externally publishedYes

Keywords

  • approximation error
  • convergence rates
  • density estimation
  • maximum likelihood
  • mixture models

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