Displaying similar documents to “Adaptive estimation of a quadratic functional of a density by model selection”

Density estimation with quadratic loss: a confidence intervals method

Pierre Alquier (2008)

ESAIM: Probability and Statistics

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We propose a feature selection method for density estimation with quadratic loss. This method relies on the study of unidimensional approximation models and on the definition of confidence regions for the density thanks to these models. It is quite general and includes cases of interest like detection of relevant wavelets coefficients or selection of support vectors in SVM. In the general case, we prove that every selected feature actually improves the performance of the estimator....

Model selection for estimating the non zero components of a Gaussian vector

Sylvie Huet (2006)

ESAIM: Probability and Statistics

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We propose a method based on a penalised likelihood criterion, for estimating the number on non-zero components of the mean of a Gaussian vector. Following the work of Birgé and Massart in Gaussian model selection, we choose the penalty function such that the resulting estimator minimises the Kullback risk.

Semiparametric deconvolution with unknown noise variance

Catherine Matias (2002)

ESAIM: Probability and Statistics

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This paper deals with semiparametric convolution models, where the noise sequence has a gaussian centered distribution, with unknown variance. Non-parametric convolution models are concerned with the case of an entirely known distribution for the noise sequence, and they have been widely studied in the past decade. The main property of those models is the following one: the more regular the distribution of the noise is, the worst the rate of convergence for the estimation of the signal’s...

On pointwise adaptive curve estimation based on inhomogeneous data

Stéphane Gaïffas (2007)

ESAIM: Probability and Statistics

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We want to recover a signal based on noisy inhomogeneous data (the amount of data can vary strongly on the estimation domain). We model the data using nonparametric regression with random design, and we focus on the estimation of the regression at a fixed point with little, or much data. We propose a method which adapts both to the local amount of data (the design density is unknown) and to the local smoothness of the regression function. The procedure consists ...

Exact adaptive pointwise estimation on Sobolev classes of densities

Cristina Butucea (2001)

ESAIM: Probability and Statistics

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The subject of this paper is to estimate adaptively the common probability density of n independent, identically distributed random variables. The estimation is done at a fixed point x 0 ∈ ℝ , over the density functions that belong to the Sobolev class W n ( β , L ) . We consider the adaptive problem setup, where the regularity parameter β is unknown and varies in a given set B n . A sharp adaptive estimator is obtained, and the explicit asymptotical constant, associated to its rate of convergence is found. ...

Model selection for regression on a random design

Yannick Baraud (2002)

ESAIM: Probability and Statistics

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We consider the problem of estimating an unknown regression function when the design is random with values in ℝ k . Our estimation procedure is based on model selection and does not rely on any prior information on the target function. We start with a collection of linear functional spaces and build, on a data selected space among this collection, the least-squares estimator. We study the performance of an estimator which is obtained by modifying this least-squares estimator on a set of...

Risk bounds for mixture density estimation

Alexander Rakhlin, Dmitry Panchenko, Sayan Mukherjee (2005)

ESAIM: Probability and Statistics

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In this paper we focus on the problem of estimating a bounded density using a finite combination of densities from a given class. We consider the Maximum Likelihood Estimator (MLE) and the greedy procedure described by Li and Barron (1999) under the additional assumption of boundedness of densities. We prove an O ( 1 n ) bound on the estimation error which does not depend on the number of densities in the estimated combination. Under the boundedness assumption, this improves the bound of Li...