Linear and convex aggregation of density estimators

  title={Linear and convex aggregation of density estimators},
  author={Philippe Rigollet and Alexandre B. Tsybakov},
We study the problem of linear and convex aggregation of M estimators of a density with respect to the mean squared risk. We provide procedures for linear and convex aggregation and we prove oracle inequalities for their risks. We also obtain lower bounds showing that these procedures are rate optimal in a minimax sense. As an example, we apply general results to aggregation of multivariate kernel density estimators with different bandwidths. We show that linear and convex aggregates mimic the… CONTINUE READING
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Are Bayes rules consistent in information? In: Open Problems in Communication and Computation, T.M.Cover and B.Gopinath, eds

  • A. Barron
  • 1987
Highly Influential
7 Excerpts

Data Driven Kernel Choice in Non-parametric Curve Estimation. PhD Thesis, Technische Universität Braunschweig

  • C. Dalelane
  • 2004
Highly Influential
2 Excerpts

On sharp adaptive estimation of multivariate curves

  • S. Efromovich
  • Math. Metods of Statist.,
  • 2000
Highly Influential
1 Excerpt

Optimal rates and constants in L2-minimax estimation of probability density functions

  • M. Schipper
  • Math. Meth. Statist.,
  • 1996
Highly Influential
1 Excerpt

Kernel Smoothing

  • M. P. Wand, M. C. Jones
  • 1995
Highly Influential
3 Excerpts

Nonparametric estimation of smooth probability densties in L2

  • G. K. Golubev
  • Problems of Information Transmission,
  • 1992
Highly Influential
2 Excerpts

LAN in nonparametric estimation of functions and lower bounds for quadratic risks

  • G. K. Golubev
  • Theory Probab. Appl.,
  • 1991
Highly Influential
1 Excerpt

On estimating a density using Hellinger distance and some other strange facts

  • L. Birgé
  • Probab. Theory Relat. Fields,
  • 1986
Highly Influential
1 Excerpt

From ǫ - entropy to KL - entropy : analysis of minimum information complexity density estimation

  • T. Zhang
  • Ann . Statist .
  • 2006

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