Filters








53 Hits in 2.0 sec

Adaptive density deconvolution with dependent inputs [article]

Fabienne Comte, Marie-Luce Taupin
2006 arXiv   pre-print
In the convolution model Z_i=X_i+ ϵ_i, we give a model selection procedure to estimate the density of the unobserved variables (X_i)_1 ≤ i ≤ n, when the sequence (X_i)_i ≥ 1 is strictly stationary but not necessarily independent. This procedure depends on wether the density of ϵ_i is super smooth or ordinary smooth. The rates of convergence of the penalized contrast estimators are the same as in the independent framework, and are minimax over most classes of regularity on R. Our results apply
more » ... mixing sequences, but also to many other dependent sequences. When the errors are super smooth, the condition on the dependence coefficients is the minimal condition of that type ensuring that the sequence (X_i)_i ≥ 1 is not a long-memory process.
arXiv:math/0606166v1 fatcat:4a7fhb5fi5hfbhr37r5qxyptr4

Finite sample penalization in adaptive density deconvolution [article]

Fabienne Comte, Marie-Luce Taupin
2006 arXiv   pre-print
We consider the problem of estimating the density g of identically distributed variables X_i, from a sample Z_1, ..., Z_n where Z_i=X_i+σϵ_i, i=1, ..., n and σϵ_i is a noise independent of X_i with known density σ^-1f_ϵ(./σ). We generalize adaptive estimators, constructed by a model selection procedure, described in Comte et al. (2005). We study numerically their properties in various contexts and we test their robustness. Comparisons are made with respect to deconvolution kernel estimators,
more » ... specification of errors, dependency,... It appears that our estimation algorithm, based on a fast procedure, performs very well in all contexts.
arXiv:math/0601098v1 fatcat:ldka2nbkhrhihav5mtoh5cavom

Adaptive density estimation for general ARCH models [article]

Fabienne Comte, Marie-Luce Taupin
2006 arXiv   pre-print
We consider a model Y_t=σ_tη_t in which (σ_t) is not independent of the noise process (η_t), but σ_t is independent of η_t for each t. We assume that (σ_t) is stationary and we propose an adaptive estimator of the density of (σ^2_t) based on the observations Y_t. Under various dependence structures, the rates of this nonparametric estimator coincide with the minimax rates obtained in the i.i.d. case when (σ_t) and (η_t) are independent, in all cases where these minimax rates are known. The
more » ... ts apply to various linear and non linear ARCH processes.
arXiv:math/0609745v1 fatcat:xbxx4pus5fhivodqzgtbn7okoq

Penalized contrast estimator for adaptive density deconvolution [article]

Fabienne Comte, Marie-Luce Taupin
2006 arXiv   pre-print
The authors consider the problem of estimating the density g of independent and identically distributed variables X_i, from a sample Z_1, ..., Z_n where Z_i=X_i+σϵ_i, i=1, ..., n, ϵ is a noise independent of X, with σϵ having known distribution. They present a model selection procedure allowing to construct an adaptive estimator of g and to find non-asymptotic bounds for its L_2(R)-risk. The estimator achieves the minimax rate of convergence, in most cases where lowers bounds are available. A
more » ... mulation study gives an illustration of the good practical performances of the method.
arXiv:math/0601091v1 fatcat:zncdtnenvbhbjghyhec5igo4ka

Model selection in logistic regression [article]

Marius Kwemou, Marie-Luce Taupin (Unité MIAJ, LaMME), Anne-Sophie Tocquet
2015 arXiv   pre-print
This paper is devoted to model selection in logistic regression. We extend the model selection principle introduced by Birg\'e and Massart (2001) to logistic regression model. This selection is done by using penalized maximum likelihood criteria. We propose in this context a completely data-driven criteria based on the slope heuristics. We prove non asymptotic oracle inequalities for selected estimators. Theoretical results are illustrated through simulation studies.
arXiv:1508.07537v1 fatcat:vyvhdckfb5fovi225yeierftmq

Estimation in autoregressive model with measurement error [article]

Jérôme Dedecker, Marie-Luce Taupin
2011 arXiv   pre-print
The first part in Var (S n (θ 0 )) j is controlled as in Butucea and Taupin (?)  ...  Note that those results do not require the Markov chain to be absolutely regular as it is the case in Comte and Taupin (?).  ...  More precisely, we start from Study of the bias Since It follows that for j = 1, · · · , d, Study of the variance For the study of the variance we combine the proof in Butucea and Taupin (?)  ... 
arXiv:1105.1310v2 fatcat:qhlsoinbczhzzdbgox3gc3twlq

Metamodel construction for sensitivity analysis

Sylvie Huet, Marie-Luce Taupin, Jean-François Coeurjolly, Adeline Leclercq-Samson
2017 ESAIM Proceedings and Surveys  
We propose to estimate a metamodel and the sensitivity indices of a complex model m in the Gaussian regression framework. Our approach combines methods for sensitivity analysis of complex models and statistical tools for sparse non-parametric estimation in multivariate Gaussian regression model. It rests on the construction of a metamodel for aproximating the Hoeffding-Sobol decomposition of m. This metamodel belongs to a reproducing kernel Hilbert space constructed as a direct sum of Hilbert
more » ... aces leading to a functional ANOVA decomposition. The estimation of the metamodel is carried out via a penalized least-squares minimization allowing to select the subsets of variables that contribute to predict the output. It allows to estimate the sensitivity indices of m. We establish an oracle-type inequality for the risk of the estimator, describe the procedure for estimating the metamodel and the sensitivity indices, and assess the performances of the procedure via a simulation study. Résumé. Nous considérons l'estimation d'un méta-modèle d'un modèle complexe m à partir des ob- servations d'un n-échantillon dans un modèle de régression gaussien. Nous en déduisons une estimation des indices de sensibilité de m. Notre approche combine les méthodes d'analyse de sensibilité de modèles complexes et les outils statistiques de l'estimation non-paramétrique en régression multivariée. Elle repose sur la construction d'un méta-modèle qui approche la décomposition de Hoeffding-Sobol de m. Ce méta-modèle appartient à un espace de Hilbert à noyau reproduisant qui est lui-même la somme directe d'espaces de Hilbert, permettant ainsi une décomposition de type ANOVA. On en déduit des estimateurs des indices de sensibilité de m. Nous établissons une inégalité de type oracle pour le risque de l'estimateur, nous décrivons la procédure pour estimer le méta-modèle et les indices de sensibilité, et évaluons les performances de notre méthode à l'aide d'une étude de simulations.
doi:10.1051/proc/201760027 fatcat:ibziuuefrfed7o4wgnamdlsuqq

Penalized contrast estimator for adaptive density deconvolution

Fabienne Comte, Yves Rozenholc, Marie-Luce Taupin
2006 Canadian journal of statistics  
The authors consider the problem of estimating the density g of independent and identically distributed variables Xi, from a sample Z1, . . . , Zn where Zi = Xi + σεi, i = 1, . . . , n, ε is a noise independent of X, with σε having known distribution. They present a model selection procedure allowing to construct an adaptive estimator of g and to find non-asymptotic bounds for its L2(R)-risk. The estimator achieves the minimax rate of convergence, in most cases where lowers bounds are
more » ... A simulation study gives an illustration of the good practical performances of the method. Déconvolution adaptative de densité par contraste pénalisé. Résumé : Les auteurs considèrent le problème de déconvolution c'est-à-dire de l'estimation de la densité de variables aléatoires identiquement distribuées Xi,à partir de l'observation de Zi où Zi = Xi + σεi, pour i = 1, . . . , n, où les erreurs σεi sont de densité connue. Par une procédure de sélection de modèles qui permet d'obtenir des bornes de risque non asymptotiques, ils construisent un estimateur adaptatif de la densité des Xi. L'estimateur atteint de façon automatique la vitesse minimax dans la plupart des cas, que les erreurs ou la densitéà estimer soient peu ou très régulières. Uneétude par simulation illustre les bonnes performances pratiques de la méthode.
doi:10.1002/cjs.5550340305 fatcat:vifejmvw6feftiruyizq3fsd5u

Adaptive kernel estimation of the baseline function in the Cox model, with high-dimensional covariates [article]

Agathe Guilloux, Marie-Luce Taupin
2015 arXiv   pre-print
The aim of this article is to propose a novel kernel estimator of the baseline function in a general high-dimensional Cox model, for which we derive non-asymptotic rates of convergence. To construct our estimator, we first estimate the regression parameter in the Cox model via a Lasso procedure. We then plug this estimator into the classical kernel estimator of the baseline function, obtained by smoothing the so-called Breslow estimator of the cumulative baseline function. We propose and study
more » ... n adaptive procedure for selecting the bandwidth, in the spirit of Gold-enshluger and Lepski (2011). We state non-asymptotic oracle inequalities for the final estimator, which reveal the reduction of the rates of convergence when the dimension of the covariates grows.
arXiv:1507.01397v1 fatcat:wo5hymz3yjdcdisxbpi7zn23re

Estimation in autoregressive model with measurement error

Jérôme Dedecker, Adeline Samson, Marie-Luce Taupin
2014 E S A I M: Probability & Statistics  
To our knowledge, the only paper which gives a consistent estimator is the paper by Comte and Taupin (2001) .  ...  Note that those results do not require the Markov chain to be absolutely regular as it is the case in Comte and Taupin (2001) .  ... 
doi:10.1051/ps/2013037 fatcat:kmx24xuc5ncnnlkdrybkvj75l4

Estimation of the hazard function in a semiparametric model with covariate measurement error

Marie-Laure Martin-Magniette, Marie-Luce Taupin
2009 E S A I M: Probability & Statistics  
Extension of the estimation procedure : a second estimator θ 2 Marie-Luce TAUPIN Laboratoire MAP5, UMR 8145, Université Paris Descartes 45, rue des Saint Pères, 75006 Paris, France e-mail : marie-luce.taupin  ... 
doi:10.1051/ps:2008004 fatcat:nrtkb4cm6zcsnahapdzdn6m76i

Risk upper bounds for RKHS ridge group sparse estimator in the regression model with non-Gaussian and non-bounded error [article]

Halaleh Kamari, Sylvie Huet, Marie-Luce Taupin
2020 arXiv   pre-print
Hoeffding 1948) , (Sobol 1993) , (van der Vaart 1998)), m(X) = m 0 + v∈P m v (X v ), (3) where m 0 is a constant. * Halaleh Kamari, Université Paris-Saclay, France, @, Sylvie Huet, INRAE, France, @, Marie-Luce  ...  Taupin, Université Evry Val d'Essonne, France, @.  ... 
arXiv:2009.11646v1 fatcat:wusyu4y6wjhbpiyeslve4alozm

Adaptive kernel estimation of the baseline function in the Cox model with high-dimensional covariates

Agathe Guilloux, Sarah Lemler, Marie-Luce Taupin
2016 Journal of Multivariate Analysis  
We propose a novel kernel estimator of the baseline function in a general highdimensional Cox model, for which we derive non-asymptotic rates of convergence. To construct our estimator, we first estimate the regression parameter in the Cox model via a LASSO procedure. We then plug this estimator into the classical kernel estimator of the baseline function, obtained by smoothing the so-called Breslow estimator of the cumulative baseline function. We propose and study an adaptive procedure for
more » ... ecting the bandwidth, in the spirit of Goldenshluger and Lepski [14] . We state non-asymptotic oracle inequalities for the final estimator, which leads to a reduction in the rate of convergence when the dimension of the covariates grows.
doi:10.1016/j.jmva.2016.03.002 fatcat:lsprggamwnh3bmwydojctvxbfa

Adaptive estimation of the baseline hazard function in the Cox model by model selection, with high-dimensional covariates

Agathe Guilloux, Sarah Lemler, Marie-Luce Taupin
2016 Journal of Statistical Planning and Inference  
The purpose of this article is to provide an adaptive estimator of the baseline function in the Cox model with high-dimensional covariates. We consider a two-step procedure : first, we estimate the regression parameter of the Cox model via a Lasso procedure based on the partial log-likelihood, secondly, we plug this Lasso estimator into a least-squares type criterion and then perform a model selection procedure to obtain an adaptive penalized contrast estimator of the baseline function. Using
more » ... n-asymptotic estimation results stated for the Lasso estimator of the regression parameter, we establish a non-asymptotic oracle inequality for this penalized contrast estimator of the baseline function, which highlights the discrepancy of the rate of convergence when the dimension of the covariates increases.
doi:10.1016/j.jspi.2015.11.005 fatcat:rwlwbt565jh75j4f3yf4nhqvti

Adaptive estimation of the baseline hazard function in the Cox model by model selection, with high-dimensional covariates [article]

Agathe Guilloux, Marie-Luce Taupin
2015 arXiv   pre-print
The purpose of this article is to provide an adaptive estimator of the baseline function in the Cox model with high-dimensional covariates. We consider a two-step procedure : first, we estimate the regression parameter of the Cox model via a Lasso procedure based on the partial log-likelihood, secondly, we plug this Lasso estimator into a least-squares type criterion and then perform a model selection procedure to obtain an adaptive penalized contrast estimator of the baseline function. Using
more » ... n-asymptotic estimation results stated for the Lasso estimator of the regression parameter, we establish a non-asymptotic oracle inequality for this penalized contrast estimator of the baseline function, which highlights the discrepancy of the rate of convergence when the dimension of the covariates increases.
arXiv:1503.00226v2 fatcat:2guhtxskl5henfqi53snwcjloi
« Previous Showing results 1 — 15 out of 53 results