Displaying similar documents to “Adaptive density estimation for clustering with gaussian mixtures”

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...

Semiparametric deconvolution with unknown noise variance

Catherine Matias (2010)

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...

Partition-based conditional density estimation

S. X. Cohen, E. Le Pennec (2013)

ESAIM: Probability and Statistics

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We propose a general partition-based strategy to estimate conditional density with candidate densities that are piecewise constant with respect to the covariate. Capitalizing on a general penalized maximum likelihood model selection result, we prove, on two specific examples, that the penalty of each model can be chosen roughly proportional to its dimension. We first study a strategy in which the densities are chosen piecewise conditional according to the variable. We then consider Gaussian...

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...

Adaptive estimation of the stationary density of discrete and continuous time mixing processes

Fabienne Comte, Florence Merlevède (2010)

ESAIM: Probability and Statistics

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In this paper, we study the problem of non parametric estimation of the stationary marginal density of an or a -mixing process, observed either in continuous time or in discrete time. We present an unified framework allowing to deal with many different cases. We consider a collection of finite dimensional linear regular spaces. We estimate using a projection estimator built on a data driven selected linear space among the collection. This data driven choice is performed the minimization...

Data-driven penalty calibration: A case study for gaussian mixture model selection

Cathy Maugis, Bertrand Michel (2011)

ESAIM: Probability and Statistics

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In the companion paper [C. Maugis and B. Michel, A non asymptotic penalized criterion for Gaussian mixture model selection. 15 (2011) 41–68] , a penalized likelihood criterion is proposed to select a Gaussian mixture model among a specific model collection. This criterion depends on unknown constants which have to be calibrated in practical situations. A “slope heuristics” method is described and experimented to deal with this practical problem. In a model-based clustering context,...

Adaptive estimation of a density function using beta kernels

Karine Bertin, Nicolas Klutchnikoff (2014)

ESAIM: Probability and Statistics

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In this paper we are interested in the estimation of a density − defined on a compact interval of ℝ− from independent and identically distributed observations. In order to avoid boundary effect, beta kernel estimators are used and we propose a procedure (inspired by Lepski’s method) in order to select the bandwidth. Our procedure is proved to be adaptive in an asymptotically minimax framework. Our estimator is compared with both the cross-validation algorithm and the oracle estimator...