Journal•ISSN: 1262-3318
Esaim: Probability and Statistics
EDP Sciences
About: Esaim: Probability and Statistics is an academic journal published by EDP Sciences. The journal publishes majorly in the area(s): Estimator & Central limit theorem. It has an ISSN identifier of 1262-3318. Over the lifetime, 562 publications have been published receiving 9835 citations. The journal is also known as: European series in applied and industrial mathematics. Probability and statistics (Online) & P&S ESAIM.
Papers published on a yearly basis
Papers
More filters
TL;DR: The last few years have witnessed important new developments in the theory and practice of pattern classification, see as discussed by the authors for a survey of the main new ideas that have lead to these important recent developments.
Abstract: The last few years have witnessed important new developments in the theory and practice of pattern classification. We intend to survey some of the main new ideas that have lead to these important recent developments. Resume. Durant ces dernieres annees, la theorie et la pratique de la reconnaissance des formes ont ´e marquees par des developpements originaux. Ce survol presente certaines des principales idees novatrices qui ont conduitces developpements importants.
569 citations
TL;DR: In this article, a new and simple approach to some of the deviation inequalities for product measures deeply investigated by M. Talagrand in the recent years is presented, based on functional inequalities of Poincare and logarithmic Sobolev type and iteration of these inequalities.
Abstract: We present a new and simple approach to some of the deviation inequalities for product measures deeply investigated by M. Talagrand in the recent years. Our method is based on functional inequalities of Poincare and logarithmic Sobolev type and iteration of these inequalities. In particular, we establish with theses tools sharp deviation inequalities from the mean on norms of sums of independent random vectors and empirical processes. Concentration for the Hamming distance may also be deduced from this approach.
321 citations
TL;DR: The stochastic approximation version of EM (SAEM) proposed by Delyon et al. as discussed by the authors is a powerful alternative to EM when the E-step is intractable, and convergence of SAEM toward a maximum of the observed likelihood is established when the unobserved data are simulated at each iteration under the conditional distribution.
Abstract: The stochastic approximation version of EM (SAEM) proposed by Delyon et al. (1999) is a powerful alternative to EM when the E-step is intractable. Convergence of SAEM toward a maximum of the observed likelihood is established when the unobserved data are simulated at each iteration under the conditional distribution. We show that this very restrictive assumption can be weakened. Indeed, the results of Benveniste et al. for stochastic approximation with Markovian perturbations are used to establish the convergence of SAEM when it is coupled with a Markov chain Monte-Carlo procedure. This result is very useful for many practical applications. Applications to the convolution model and the change-points model are presented to illustrate the proposed method.
286 citations
TL;DR: In this article, the authors consider the statistical estimation of the Sobol sensitivity index from a finite sample of model outputs and show that one of these estimators has an optimal asymptotic variance.
Abstract: Many mathematical models involve input parameters, which are not precisely known. Global sensitivity analysis aims to identify the parameters whose uncertainty has the largest impact on the variability of a quantity of interest (output of the model). One of the statistical tools used to quantify the influence of each input variable on the output is the Sobol sensitivity index. We consider the statistical estimation of this index from a finite sample of model outputs: we present two estimators and state a central limit theorem for each. We show that one of these estimators has an optimal asymptotic variance. We also generalize our results to the case where the true output is not observable, and is replaced by a noisy version.
197 citations
TL;DR: In this paper, it was shown that the LAN property holds under quite weak smoothness assumptions, with an explicit limiting Fisher information, and the rate at which this convergence takes place is 1 = p n (as when there is no measurement error) when n goes fast enough to 0, namely nn is bounded.
Abstract: We consider a diusion process X which is observed at timesi=n for i =0 ; 1;::: ;n, each observation being subject to a measurement error. All errors are independent and centered Gaussian with known variance n. There is an unknown parameter within the diusion coecient, to be estimated. In this rst paper the case when X is indeed a Gaussian martingale is examined: we can prove that the LAN property holds under quite weak smoothness assumptions, with an explicit limiting Fisher information. What is perhaps the most interesting is the rate at which this convergence takes place: it is 1= p n (as when there is no measurement error) when n goes fast enough to 0, namely nn is bounded. Otherwise, and provided the sequence n itself is bounded, the rate is (n=n) 1=4 .I n particular if n = does not depend on n ,w e get ar aten 1=4 .
168 citations