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Inequalities for absolutely regular sequences: application to density estimation
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  • Published: April 1997

Inequalities for absolutely regular sequences: application to density estimation

  • Gabrielle Viennet1 

Probability Theory and Related Fields volume 107, pages 467–492 (1997)Cite this article

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Abstract.

This paper investigates the problem of density estimation for absolutely regular observations. In a first part, we state two important results: a new variance inequality and a Rosenthal type inequality. This allows us to study the ? p -integrated risk, p≧ 2, of a large class of density estimators including kernel or projection estimators. Under the summability condition on the mixing coefficients ∑ k≧ 0 (k+1) p− 2 β k <∞, the rates obtained are those known to be optimal in the independent setting.

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Authors and Affiliations

  1. Laboratoire de modélisation stochastique et statistique, Bât. 425, Université Paris Sud, F-91405 Orsay Cedex, France (e-mail: gabrielle.viennet@math.u-psud.fr), , , , , , FR

    Gabrielle Viennet

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  1. Gabrielle Viennet
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Received: 17 October 1995 / In revised form: 26 October 1996

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Viennet, G. Inequalities for absolutely regular sequences: application to density estimation. Probab Theory Relat Fields 107, 467–492 (1997). https://doi.org/10.1007/s004400050094

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  • Issue Date: April 1997

  • DOI: https://doi.org/10.1007/s004400050094

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  • Mathematics Subject Classification (1991): 62G05
  • 60K99
  • 60F25
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