Displaying similar documents to “Recursive bias estimation for multivariate regression smoothers”

Model selection for regression on a random design

Yannick Baraud (2010)

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...

Uniform strong consistency of a frontier estimator using kernel regression on high order moments

Stéphane Girard, Armelle Guillou, Gilles Stupfler (2014)

ESAIM: Probability and Statistics

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We consider the high order moments estimator of the frontier of a random pair, introduced by [S. Girard, A. Guillou and G. Stupfler, 116 (2013) 172–189]. In the present paper, we show that this estimator is strongly uniformly consistent on compact sets and its rate of convergence is given when the conditional cumulative distribution function belongs to the Hall class of distribution functions.

Model selection for (auto-)regression with dependent data

Yannick Baraud, F. Comte, G. Viennet (2010)

ESAIM: Probability and Statistics

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In this paper, we study the problem of non parametric estimation of an unknown regression function from dependent data with sub-Gaussian errors. As a particular case, we handle the autoregressive framework. For this purpose, we consider a collection of finite dimensional linear spaces ( linear spaces spanned by wavelets or piecewise polynomials on a possibly irregular grid) and we estimate the regression function by a least-squares estimator built on a data driven selected linear space...

An ℓ1-oracle inequality for the Lasso in finite mixture gaussian regression models

Caroline Meynet (2013)

ESAIM: Probability and Statistics

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We consider a finite mixture of Gaussian regression models for high-dimensional heterogeneous data where the number of covariates may be much larger than the sample size. We propose to estimate the unknown conditional mixture density by an -penalized maximum likelihood estimator. We shall provide an -oracle inequality satisfied by this Lasso estimator with the Kullback–Leibler loss. In particular, we give a condition on the regularization parameter of...

Nonparametric estimation of the density of the alternative hypothesis in a multiple testing setup. Application to local false discovery rate estimation

Van Hanh Nguyen, Catherine Matias (2014)

ESAIM: Probability and Statistics

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In a multiple testing context, we consider a semiparametric mixture model with two components where one component is known and corresponds to the distribution of -values under the null hypothesis and the other component is nonparametric and stands for the distribution under the alternative hypothesis. Motivated by the issue of local false discovery rate estimation, we focus here on the estimation of the nonparametric unknown component in the mixture, relying on a preliminary estimator...