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Dive into the research topics where Jérôme Dedecker is active.

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Featured researches published by Jérôme Dedecker.


Stochastic Processes and their Applications | 2003

A New Covariance Inequality and Applications

Jérôme Dedecker; Paul Doukhan

We compare three dependence coefficients expressed in terms of conditional expectations, and we study their behaviour in various situations. Next, we give a new covariance inequality involving the weakest of those coefficients, and we compare this bound to that obtained by Rio (Ann. Inst. H. Poincare Probab. Statist. 29 (1993) 587-597) in the strongly mixing case. This new inequality is used to derive sharp limit theorems, such as Donskers invariance principle and Marcinkiewiczs strong law. As a consequence of a Burkholder-type inequality, we obtain a deviation inequality for partial sums.


Annales De L Institut Henri Poincare-probabilites Et Statistiques | 2000

On the functional central limit theorem for stationary processes

Jérôme Dedecker; Emmanuel Rio

Abstract We give a sufficient condition for a stationary sequence of square-integrable and real-valued random variables to satisfy a Donsker-type invariance principle. This condition is similar to the L 1 -criterion of Gordin for the usual central limit theorem and provides invariance principles for α-mixing or β-mixing sequences as well as stationary Markov chains. In the latter case, we present an example of a non irreducible and non α-mixing chain to which our result applies.


Annales De L Institut Henri Poincare-probabilites Et Statistiques | 2010

Some almost sure results for unbounded functions of intermittent maps and their associated Markov chains

Jérôme Dedecker; Sébastien Gouëzel; Florence Merlevède

We consider a large class of piecewise expanding maps T of [0; 1] with a neutral xed point, and their associated Markov chain Yi whose transition kernel is the PerronFrobenius operator of T with respect to the absolutely continuous invariant probability measure. We give a large class of unbounded functions f for which the partial sums of f T i satisfy both a central limit theorem and a bounded law of the iterated logarithm. For the same class, we prove that the partial sums of f(Yi) satisfy a strong invariance principle. When the class is larger, so that the partial sums of f T i may belong to the domain of normal attraction of a stable law of index p2 (1; 2), we show that the almost sure rates of convergence in the strong law of large numbers are the same as in the corresponding i.i.d. case.


Annales De L Institut Henri Poincare-probabilites Et Statistiques | 2008

On mean central limit theorems for stationary sequences

Jérôme Dedecker; Emmanuel Rio

In this paper, we give estimates of the minimal


Electronic Journal of Statistics | 2011

Deconvolution for the Wasserstein Metric and Geometric Inference

Claire Caillerie; Frédéric Chazal; Jérôme Dedecker; Bertrand Michel

{\mathbb{L}}^1


Theory of Probability and Its Applications | 2008

Convergence Rates in the Law of Large Numbers for Banach-Valued Dependent Variables

Jérôme Dedecker; Florence Merlevède

distance between the distribution of the normalized partial sum and the limiting Gaussian distribution for stationary sequences satisfying projective criteria in the style of Gordin or weak dependence conditions.


Bernoulli | 2011

Invariance principles for linear processes with application to isotonic regression

Jérôme Dedecker; Florence Merlevède; Magda Peligrad

This paper is a short presentation of recent results about Wasserstein deconvolution for topological inference published in [1]. A distance function to measures has been defined in [2] to answer geometric inference problems in a probabilistic setting. According to their result, the topological properties of a shape can be recovered by using the distance to a known measure ν, if ν is close enough to a measure μ for he Wasserstein distance W 2. Given a point cloud, a natural candidate for ν is the empirical measure μ n . Nevertheless, in many situations the data points are not located on the geometric shape but in the neighborhood of it, and μ n can be too far from μ. In a deconvolution framework, we consider a slight modification of the classical kernel deconvolution estimator, and we give a consistency result and rates of convergence for this estimator. Some simulated experiments illustrate the deconvolution method and its application to geometric inference on various shapes and with various noise distributions.


Mathematical Methods of Statistics | 2008

Adaptive density deconvolution with dependent inputs

Fabienne Comte; Jérôme Dedecker; Marie-Luce Taupin

We extend Marcinkievicz–Zygmund strong laws of large numbers for martingales to weakly dependent random variables with values in smooth Banach spaces. The conditions are expressed in terms of conditional expectations. In the case of Hilbert spaces, we show that our conditions are weaker than optimal ones for strongly mixing sequences (which were previously known for real-valued variables only). As a consequence, we give rates of convergence for Cramer–von Mises statistics and for the empirical estimator of the covariance operator of a Hilbert-valued autoregressive process.


Annales De L Institut Henri Poincare-probabilites Et Statistiques | 2009

Moderate deviations for stationary sequences of bounded random variables

Jérôme Dedecker; Florence Merlevède; Magda Peligrad; Sergey Utev

In this paper, we prove maximal inequalities and study the functional central limit theorem for the partial sums of linear processes generated by dependent innovations. Due to the general weights, these processes can exhibit long-range dependence and the limiting distribution is a fractional Brownian motion. The proofs are based on new approximations by a linear process with martingale difference innovations. The results are then applied to study an estimator of the isotonic regression when the error process is a (possibly long-range dependent) time series.


Archive | 2002

Maximal Inequalities and Empirical Central Limit Theorems

Jérôme Dedecker; Sana Louhichi

In the convolution model Zi = Xi + εi, we give a model selection procedure to estimate the density of the unobserved variables (Xi)1≤i≤n, when the sequence (Xi)i≥1 is strictly stationary but not necessarily independent. This procedure depends on whether the density of the ɛi is supersmooth 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 regularity classes on ℝ. Our results apply to mixing sequences, but also to many other dependent sequences. When the errors are supersmooth, the condition on the dependence coefficients is the minimal condition of that type ensuring that the sequence (Xi)i≥1 is not a long-memory process.

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Magda Peligrad

University of Cincinnati

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Christophe Cuny

University of New Caledonia

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Marie-Luce Taupin

Institut national de la recherche agronomique

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Françoise Pène

Centre national de la recherche scientifique

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Xiequan Fan

Centre national de la recherche scientifique

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Christophe Cuny

University of New Caledonia

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