Why L 1 view and what is next?

László Györfi; Adam Krzyżak

Kybernetika (2011)

  • Volume: 47, Issue: 6, page 840-854
  • ISSN: 0023-5954

Abstract

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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 L 1 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 L 1 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.

How to cite

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Györfi, László, and Krzyżak, Adam. "Why $L_1$ view and what is next?." Kybernetika 47.6 (2011): 840-854. <http://eudml.org/doc/197111>.

@article{Györfi2011,
abstract = {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 $L_1$ 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 $L_1$ 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.},
author = {Györfi, László, Krzyżak, Adam},
journal = {Kybernetika},
keywords = {Cencov’s comments; inverse problems in distribution estimation; $L_1$ density estimation; variational distance; $\phi $-divergence; Cencov's comments; inverse problems in distribution estimation; density estimation; variational distance; -divergence},
language = {eng},
number = {6},
pages = {840-854},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Why $L_1$ view and what is next?},
url = {http://eudml.org/doc/197111},
volume = {47},
year = {2011},
}

TY - JOUR
AU - Györfi, László
AU - Krzyżak, Adam
TI - Why $L_1$ view and what is next?
JO - Kybernetika
PY - 2011
PB - Institute of Information Theory and Automation AS CR
VL - 47
IS - 6
SP - 840
EP - 854
AB - 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 $L_1$ 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 $L_1$ 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.
LA - eng
KW - Cencov’s comments; inverse problems in distribution estimation; $L_1$ density estimation; variational distance; $\phi $-divergence; Cencov's comments; inverse problems in distribution estimation; density estimation; variational distance; -divergence
UR - http://eudml.org/doc/197111
ER -

References

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