A Robbins-Monro procedure for estimation in semiparametric regression models

This paper is devoted to the parametric estimation of a shift together with the nonparametric estimation of a regression function in a semiparametric regression model. We implement a very efficient and easy to handle Robbins-Monro procedure. On the one hand, we propose a stochastic algorithm similar to that of Robbins-Monro in order to estimate the shift parameter. A preliminary evaluation of the regression function is not necessary to estimate the shift parameter. On the other hand, we make use of a recursive Nadaraya-Watson estimator for the estimation of the regression function. This kernel estimator takes into account the previous estimation of the shift parameter. We establish the almost sure convergence for both Robbins-Monro and Nadaraya--Watson estimators. The asymptotic normality of our estimates is also provided. Finally, we illustrate our semiparametric estimation procedure on simulated and real data.Comment: Published in at http://dx.doi.org/10.1214/12-AOS969 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Convergence and round-off errors in a two-dimensional eigenvalue problem using spectral methods and Arnoldi-Chebyshev algorithm

An efficient way of solving 2D stability problems in fluid mechanics is to use, after discretization of the equations that cast the problem in the form of a generalized eigenvalue problem, the incomplete Arnoldi-Chebyshev method. This method preserves the banded structure sparsity of matrices of the algebraic eigenvalue problem and thus decreases memory use and CPU-time consumption. The errors that affect computed eigenvalues and eigenvectors are due to the truncation in the discretization and to finite precision in the computation of the discretized problem. In this paper we analyze those two errors and the interplay between them. We use as a test case the two-dimensional eigenvalue problem yielded by the computation of inertial modes in a spherical shell. This problem contains many difficulties that make it a very good test case. It turns out that that single modes (especially most-damped modes i.e. with high spatial frequency) can be very sensitive to round-off errors, even when apparently good spectral convergence is achieved. The influence of round-off errors is analyzed using the spectral portrait technique and by comparison of double precision and extended precision computations. Through the analysis we give practical recipes to control the truncation and round-off errors on eigenvalues and eigenvectors.Comment: 15 pages, 9 figure

Regularity criteria of almost every function in a Sobolev space

International audienceIn this paper we determine the multifractal nature of almost every function (in the prevalence setting) in a given Sobolev or Besov space according to different regularity exponents. These regularity criteria are based on local $L^p$ regularity or on wavelet coefficients and give a precise information on pointwise behavior

La fabrication des modèles de genre dans les magazines sportifs. Pratiques journalistiques et logiques de positionnement des titres, l'exemple du vélo tout terrain

La plupart des analyses portant sur les modèles de genre présents dans la presse sportive concluent à une forte conformité sexuée. Bien étudiées dans la littérature anglo-saxonne, les figures médiatiques du masculin et du féminin dans les magazines sportifs spécialisés sont particulièrement représentatives de ce que CONNELL (1987) appelle la masculinité hégémonique et l'emphasized feminity. Partant de ce constat, cette thèse confronte les résultats obtenus dans ces recherches en analysant finement les modèles de genre proposés par les revues spécialisées de Vélo Tout Terrain, activité instrumentée de pleine nature, à priori associée à des modèles féminins et masculins relativement distants des définitions les plus traditionnelles des catégories sexuées. L'analyse du corpus, basée sur les trois magazines majoritaires dans le sous-champ : Vélo Vert, VTTMag et Vélo Tout Terrain, confirme dans un premier temps la forte présence des aspects les plus extrêmes de la masculinité hégémonique et de l'emphasized feminity. Mais, certains contextes de pratique ou des statuts particuliers au sein du milieu VTT offrent aux lecteurs des modèles de genre beaucoup plus novateurs et relativement distants des représentations médiatiques traditionnelles. Etudier le milieu du VTT en se centrant sur la construction des modèles de genre dans les revues spécialisées permet de questionner le rôle des médias dans la production d'une définition légitime de l'activité, mais également de mettre en évidence la doxa (BOURDIEU, 1997) qui structure cet espace de pratique en termes de rapports sociaux de sexe. L'analyse des parcours professionnels et des pratiques journalistiques met en évidence deux " groupes " de journalistes bien distincts. Fondés sur des processus d'identification professionnelle opposés, ces deux profils entraînent des rapports plus ou moins critiques avec le milieu du VTT et avec les modèles de genre qui y sont valorisés. Par ailleurs, ces rapports sociaux de sexe s'exerçant au sein des rédactions ne permettent pas aux journalistes féminines de s'imposer. En faible nombre, dominées par leur statut de pigiste et de compagne de journaliste, elles se heurtent à la forte sociabilité masculine en vigueur dans les rédactions, véritables lieux de construction d'une " masculinité VTT ". Au-delà de l'importance du pôle de la production, le pôle éditorial, et plus particulièrement les différentes maisons d'édition, leur histoire, leur structuration influencent fortement le positionnement de chaque titre, orientant de manière importante les modes de mise en scène des modèles de genreMost of the analyses dealing with gender models in sport medias lead to the same conclusion: a strong conformity to sexual order. Widely studied in Anglo-Saxon literature, male and female media representations in specialized sport magazines are particularly representative of what CONNELL (1987) calls the hegemonic masculinity and the emphasized feminity. On this basis, this thesis compares the results of these studies by meticulously analysing the gender models presented in specialised mountain bike publications. As mountain biking is an equipped outdoor activity, it is at first sight be associated to male and female models which are quite remote from the most traditional definitions of the sex categories. The analysis of the corpus, based on three main magazines in the field: Vélo Vert, Vélo Tout Terrain and VTTMag confirms at first the strong presence of the most extreme aspects of both hegemonic masculinity and emphasized feminity. But some riding contexts or specific statuses among the Mountain Bike circle provide the readers with much more innovative gender models, quite remote from the traditional media representations. Studying the Mountain Bike circle by focusing on the gender model construction in specialised publications permits to question the role of media in the production of a legitimate definition of the activity, but also to underscore the doxa (BOURDIEU, 1997) that structures this field of practice in terms of sex social relations. The analysis of career paths and journalistic practices shows that two distinct kinds of journalists exist. Based on opposite professional identification processes, these two profiles lead to more or less critical relationships with the Mountain Bike circle and the gender models enhanced in them. Moreover, these sex social relations which prevail among the editorial staffs prevent women from being heard. Insufficient in number, weakened by their status of freelance journalist and male journalist's wife, they come up against the strong male sociability which is in force in editorial offices, genuine places of construction of a "Mountain Bike masculinity". Beyond the importance of the production unit, the publishing unit, and more precisely the different publishing houses, their history, their organization, highly influence the position of each title, strongly orientating the modes of mise en scene of gender model

On the wavelet denoising of multifractal functions

This paper is devoted to the link between the rate of convergence of functions by thresholding algorithms and the multifractal formalism. Indeed we show that once given its Besov regularity, almost every function in the prevalence sense, is approximated at the minimax rate. We also prove that when the multifractal formalism is fulfilled the corresponding functions are approximated at the minimax rate of convergence

Why minimax is not that pessimistic

International audienceIn nonparametric statistics a classical optimality criterion for estimation procedures is provided by the minimax rate of convergence. However this point of view can be subject to controversy as it requires to look for the worst behavior of an estimation procedure in a given space. The purpose of this paper is to introduce a new criterion based on generic behavior of estimators. We are here interested in the rate of convergence obtained with some classical estimators on almost every, in the sense of prevalence, function in a Besov space. We also show that generic results coincide with minimax ones in these cases