Displaying similar documents to “Density estimation with quadratic loss: a confidence intervals method”

Adaptive estimation of a quadratic functional of a density by model selection

Béatrice Laurent (2005)

ESAIM: Probability and Statistics

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We consider the problem of estimating the integral of the square of a density f from the observation of a n sample. Our method to estimate ∫ ℝ f 2 ( x ) d x is based on model selection via some penalized criterion. We prove that our estimator achieves the adaptive rates established by Efroimovich and Low on classes of smooth functions. A key point of the proof is an exponential inequality for U -statistics of order 2 due to Houdré and Reynaud.

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.

Asymptotic unbiased density estimators

Nicolas W. Hengartner, Éric Matzner-Løber (2009)

ESAIM: Probability and Statistics

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This paper introduces a computationally tractable density estimator that has the same asymptotic variance as the classical Nadaraya-Watson density estimator but whose asymptotic bias is zero. We achieve this result using a two stage estimator that applies a multiplicative bias correction to an oversmooth pilot estimator. Simulations show that our asymptotic results are available for samples as low as , where we see an improvement of as much as 20% over the traditionnal estimator. ...

Risk hull method for spectral regularization in linear statistical inverse problems

Clément Marteau (2010)

ESAIM: Probability and Statistics

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We consider in this paper the statistical linear inverse problem = + where denotes a compact operator, a noise level and a stochastic noise. The unknown function has to be recovered from the indirect measurement . We are interested in the following approach: given a family of estimators, we want to select the best possible one. In this context, the unbiased risk estimation (URE) method is rather popular. Nevertheless, it is also very unstable. Recently, Cavalier...

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 ...

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...