Bernard Bercu - Academia.edu (original) (raw)

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Jon A. Wellner

Florin Avram

Stéphane Girard

Institut National de Recherche en Informatique et Automatique (INRIA)

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Papers by Bernard Bercu

Research paper thumbnail of On the asymptotic behavior of the Nadaraya-Watson estimator associated with the recursive SIR method, in "Statistics

Abstract. We investigate the asymptotic behavior of the Nadaraya-Watson esti-mator for the estima... more Abstract. We investigate the asymptotic behavior of the Nadaraya-Watson esti-mator for the estimation of the regression function in a semiparametric regression model. On the one hand, we make use of the recursive version of the sliced inverse regression method for the estimation of the unknown parameter of the model. On the other hand, we implement a recursive Nadaraya-Watson procedure for the estimation of the regression function which takes into account the previous esti-mation of the parameter of the semiparametric regression model. We establish the almost sure convergence as well as the asymptotic normality for our Nadaraya-Watson estimator. We also illustrate our semiparametric estimation procedure on simulated data. 1.

Research paper thumbnail of Grandes déviations pour des formes quadratiques de processus gaussiens stationnaires

Comptes Rendus De L Academie Des Sciences Serie 1 Mathematique, 1996

On montre un principe de grandes deviations pour des formes quadratiques de Toeplitz de processus... more On montre un principe de grandes deviations pour des formes quadratiques de Toeplitz de processus gaussiens stationnaires centres. La fonction de taux s'obtient par la methode MEM (maximum d'entropie sur la moyenne) et par une etude fine du comportement des valeurs propres d'un produit de deux matrices de Toeplitz.

Research paper thumbnail of Concentration inequalities, large and moderate deviations for self-normalized empirical processes

The Annals of Probability, 2002

Research paper thumbnail of On the convergence of moments in the almost sure central limit theorem for stochastic approximation algorithms

ESAIM: Probability and Statistics, 2013

Research paper thumbnail of A new approach on recursive and non-recursive SIR methods

Journal of the Korean Statistical Society, 2012

Research paper thumbnail of Asymptotic analysis for bifurcating autoregressive processes via a martingale approach

We study the asymptotic behavior of the least squares estimators of the unknown parameters of gen... more We study the asymptotic behavior of the least squares estimators of the unknown parameters of general pth-order bifurcating autoregressive processes. Under very weak assumptions on the driven noise of the process, namely conditional pair-wise independence and suitable moment conditions, we establish the almost sure convergence of our estimators together with the quadratic strong law and the central limit theorem. All our analysis relies on non-standard asymptotic results for martingales.

Research paper thumbnail of Almost sure central limit theorems on the Wiener space

Research paper thumbnail of Large deviations for Gaussian stationary processes and semi-classical analysis

In this paper, we obtain a large deviation principle for quadratic forms of Gaussian stationary p... more In this paper, we obtain a large deviation principle for quadratic forms of Gaussian stationary processes. It is established by the conjunction of a result of Roch and Silbermann on the spectrum of products of Toeplitz matrices together with the analysis of large deviations carried out by Gamboa, Rouault and the first author. An alternative proof of the needed result on Toeplitz matrices, based on semi-classical analysis, is also provided. Keywords Large deviations • Gaussian processes • Toeplitz matrices • Distribution of eigenvalues Pn(x 0 , x 1 , x 2 ,. . .

Research paper thumbnail of On the asymptotic behaviour of the recursive Nadaraya–Watson estimator associated with the recursive sliced inverse regression method

Statistics, 2014

We investigate the asymptotic behaviour of the recursive Nadaraya-Watson estimator for the estima... more We investigate the asymptotic behaviour of the recursive Nadaraya-Watson estimator for the estimation of the regression function in a semiparametric regression model. On the one hand, we make use of the recursive version of the sliced inverse regression method for the estimation of the unknown parameter of the model. On the other hand, we implement a recursive Nadaraya-Watson procedure for the estimation of the regression function which takes into account the previous estimation of the parameter of the semiparametric regression model. We establish the almost sure convergence as well as the asymptotic normality for our Nadaraya-Watson estimate. We also illustrate our semiparametric estimation procedure on simulated data.

Research paper thumbnail of On the asymptotic behavior of the Nadaraya-Watson estimator associated with the recursive SIR method, in "Statistics

Abstract. We investigate the asymptotic behavior of the Nadaraya-Watson esti-mator for the estima... more Abstract. We investigate the asymptotic behavior of the Nadaraya-Watson esti-mator for the estimation of the regression function in a semiparametric regression model. On the one hand, we make use of the recursive version of the sliced inverse regression method for the estimation of the unknown parameter of the model. On the other hand, we implement a recursive Nadaraya-Watson procedure for the estimation of the regression function which takes into account the previous esti-mation of the parameter of the semiparametric regression model. We establish the almost sure convergence as well as the asymptotic normality for our Nadaraya-Watson estimator. We also illustrate our semiparametric estimation procedure on simulated data. 1.

Research paper thumbnail of Grandes déviations pour des formes quadratiques de processus gaussiens stationnaires

Comptes Rendus De L Academie Des Sciences Serie 1 Mathematique, 1996

On montre un principe de grandes deviations pour des formes quadratiques de Toeplitz de processus... more On montre un principe de grandes deviations pour des formes quadratiques de Toeplitz de processus gaussiens stationnaires centres. La fonction de taux s'obtient par la methode MEM (maximum d'entropie sur la moyenne) et par une etude fine du comportement des valeurs propres d'un produit de deux matrices de Toeplitz.

Research paper thumbnail of Concentration inequalities, large and moderate deviations for self-normalized empirical processes

The Annals of Probability, 2002

Research paper thumbnail of On the convergence of moments in the almost sure central limit theorem for stochastic approximation algorithms

ESAIM: Probability and Statistics, 2013

Research paper thumbnail of A new approach on recursive and non-recursive SIR methods

Journal of the Korean Statistical Society, 2012

Research paper thumbnail of Asymptotic analysis for bifurcating autoregressive processes via a martingale approach

We study the asymptotic behavior of the least squares estimators of the unknown parameters of gen... more We study the asymptotic behavior of the least squares estimators of the unknown parameters of general pth-order bifurcating autoregressive processes. Under very weak assumptions on the driven noise of the process, namely conditional pair-wise independence and suitable moment conditions, we establish the almost sure convergence of our estimators together with the quadratic strong law and the central limit theorem. All our analysis relies on non-standard asymptotic results for martingales.

Research paper thumbnail of Almost sure central limit theorems on the Wiener space

Research paper thumbnail of Large deviations for Gaussian stationary processes and semi-classical analysis

In this paper, we obtain a large deviation principle for quadratic forms of Gaussian stationary p... more In this paper, we obtain a large deviation principle for quadratic forms of Gaussian stationary processes. It is established by the conjunction of a result of Roch and Silbermann on the spectrum of products of Toeplitz matrices together with the analysis of large deviations carried out by Gamboa, Rouault and the first author. An alternative proof of the needed result on Toeplitz matrices, based on semi-classical analysis, is also provided. Keywords Large deviations • Gaussian processes • Toeplitz matrices • Distribution of eigenvalues Pn(x 0 , x 1 , x 2 ,. . .

Research paper thumbnail of On the asymptotic behaviour of the recursive Nadaraya–Watson estimator associated with the recursive sliced inverse regression method

Statistics, 2014

We investigate the asymptotic behaviour of the recursive Nadaraya-Watson estimator for the estima... more We investigate the asymptotic behaviour of the recursive Nadaraya-Watson estimator for the estimation of the regression function in a semiparametric regression model. On the one hand, we make use of the recursive version of the sliced inverse regression method for the estimation of the unknown parameter of the model. On the other hand, we implement a recursive Nadaraya-Watson procedure for the estimation of the regression function which takes into account the previous estimation of the parameter of the semiparametric regression model. We establish the almost sure convergence as well as the asymptotic normality for our Nadaraya-Watson estimate. We also illustrate our semiparametric estimation procedure on simulated data.

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