Why L1 view and what is next?

László Györfi, Adam Krzyzak

Research output: Contribution to journalArticle


N. N. Cencov wrote a commentary chapter included in the Appendix of the Russian translation of the Devroye and Györfi book [15] collecting some arguments supporting the L1 view of density estimation. The Cencov's work is available in Russian only and it hasn't been translated, so late Igor Vajda decided to translate the Cencov's paper and to add some remarks on the occasion of organizing the session "25 Years of the L1 Density Estimation" at the Prague Stochastics 2010 Symposium. In this paper we complete his task, i. e., we translate the Cencov's chapter and insert some remarks on the related literature focusing primarily on Igor's results. We would also like to acknowledge the excellent work of Alexandre Tsybakov who translated the Devroye and Györfi book in Russian, annotated it with valuable comments and included some related references published in Russian only.

Original languageEnglish
Pages (from-to)840-854
Number of pages15
Issue number6
Publication statusPublished - Dec 19 2011


  • Cencov's comments
  • Inverse problems in distribution estimation
  • L density estimation
  • Variational distance
  • φ-divergence

ASJC Scopus subject areas

  • Software
  • Control and Systems Engineering
  • Theoretical Computer Science
  • Information Systems
  • Artificial Intelligence
  • Electrical and Electronic Engineering

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  • Cite this

    Györfi, L., & Krzyzak, A. (2011). Why L1 view and what is next? Kybernetika, 47(6), 840-854.