Model selection via testing : an alternative to (penalized) maximum likelihood estimators
Lucien Birgé (2006)
Annales de l'I.H.P. Probabilités et statistiques
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Lucien Birgé (2006)
Annales de l'I.H.P. Probabilités et statistiques
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A. Goldenshluger, A. Juditsky, A. Tsybakov, A. Zeevi (2008)
Annales de l'I.H.P. Probabilités et statistiques
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We focus on the problem of adaptive estimation of signal singularities from indirect and noisy observations. A typical example of such a singularity is a discontinuity (change-point) of the signal or of its derivative. We develop a change-point estimator which adapts to the unknown smoothness of a nuisance deterministic component and to an unknown jump amplitude. We show that the proposed estimator attains optimal adaptive rates of convergence. A simulation study demonstrates reasonable...
Silvelyn Zwanzig (1994)
Kybernetika
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F. Comte, S. Gaïffas, A. Guilloux (2011)
Annales de l'I.H.P. Probabilités et statistiques
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We propose in this work an original estimator of the conditional intensity of a marker-dependent counting process, that is, a counting process with covariates. We use model selection methods and provide a nonasymptotic bound for the risk of our estimator on a compact set. We show that our estimator reaches automatically a convergence rate over a functional class with a given (unknown) anisotropic regularity. Then, we prove a lower bound which establishes that this rate is optimal. Lastly,...
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...
Lubomír Kubáček (2004)
Applications of Mathematics
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In nonlinear regression models an approximate value of an unknown parameter is frequently at our disposal. Then the linearization of the model is used and a linear estimate of the parameter can be calculated. Some criteria how to recognize whether a linearization is possible are developed. In the case that they are not satisfied, it is necessary to take into account either some quadratic corrections or to use the nonlinear least squares method. The aim of the paper is to find some criteria...
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.