Mohamed Chaouch

Cette thèse est consacré à l'estimation non paramétrique des quantiles géométriques conditionnels ou non et à l'analyse des données fonctionnelles. Nous nous sommes intéressés, dans un premier temps, à l'étude des quantiles géométriques. Nous avons montré, avec plusieurs simulations, qu'une étape de Transformation-retransformation est nécessaire, pour estimer le quantile géométrique, lorsqu'on s'éloigne du cadre d'une distribution sphérique. Une étude sur des données réelles a confirmée que la modélisation des données est mieux adaptée lorsqu'on utilise les quantiles géométriques à la place des quantiles mariginaux, notamment lorsque les variables qui constituent le vecteur aléatoire sont corrélées. Ensuite nous avons étudié l'estimation des quantiles géométriques lorsque les observations sont issues d'un plan de sondage. Nous avons proposé un estimateur sans biais du quantile géométrique et à l'aide des techniques de linéarisation par les...

This study was retrospective. The authors analyse the clinical, etiological and therapeutic aspects of the intestinal intussusception based on 13 adults observed over 14 years in the surgical department of the university hospital in Monastir. This disease was rare because accounted for 2.6% of all cases of intestinal obstruction. The diagnosis was made in the majority of cases during the operation (8/13). Abdominal pain was noted in all cases. The underlying pathologic processes were identified in 69%. Operation was required in every case. During the surgery, the lead point was identified in the small bowel in 12 cases and in the colon in one case. An intestinal tumor was found in four patients (39%), only one of which was malignant. Adult intussusception is an unusual cause of abdominal pain and bowel obstruction. It requires preoperative diagnosis. Operative management is always necessary because this condition is almost always secondary to definable lesion.

Necrotizing fasciitis is a rare and severe infectious disease with infectious necrosis often extending in depth to the subcutaneous tissue in the absence of rapid medical-surgical treatment. We report two cases of necrotizing fasciitis of the thigh, which underline the principle clinical and therapeutic characteristics of this often underrated disease. The first case concerns a young 21 year-old woman without remarkable medical history who, following injury from the thorn of a palm tree, developed an aerobic germ necrotizing fasciitis which regressed following medical-surgical treatment. The second case concerned a 46 year-old man suffering from diabetes and arteritis, who having presented an infection following the amputation of the large toes, developed fatal necrotizing fasciitis. This disease corresponds to infectious necrosis of the subcutaneous tissue and is essentially characterized by its rapid, occasionally violent, progression. It represents a surgical emergency and requir...

ABSTRACT Résumé Les courbes de profil moyen sont largement utilisées comme indicateurs du comportement de consommation d’électricité des clients. ÀÉlectricité de France (EDF), les profils de consommation de chaque catégorie de clients sont estimés par des courbes de charge moyennes. Malheureusement, la moyenne est très sensible à la présence des valeurs atypiques. Dans ce travail, nous proposons une alternative à la courbe moyenne: la L1‐médiane, qui est plus robuste. En présence de grandes bases de données de type courbes (les courbes de charge, par exemple), des approches par sondages sont une alternative intéressante pour estimer la courbe médiane en évitant le stockage de courbes. Nous proposons ici plusieurs stratégies d’échantillonnage et plusieurs estimateurs de la courbe médiane. Une comparaison entre les différentes stratégies est réalisée sur une population‐test. Nous développons une stratification basée sur les variables linéarisées qui améliore de façon substantielle l’estimateur par rapport au sondage aléatoire simple sans remise. Nous suggérons également un estimateur qui prend en compte l’information auxiliaire. Plusieurs directions de recherche sont envisagées.

Dans ce travail, nous nous sommes intéressées à l'estimation du quantile géométrique pour des données issues d'un plan de sondage. Nous donnons un estimateur du quan- tile géométrique basé sur le plan de sondage ainsi qu'une méthode itérative pour l'obtenir à partir des données d'échantillonnage. Sous des conditions générales, nous dérivons la variance asymptotique de l'estimateur du quantile et nous proposons un estimateur con- vergent de cette variance. Le bon comportement de l'estimateur du quantile géométrique est véri fié par une étude par simulation.

This paper deals with quantile regression of a vector response (Y in R^q, q  2) on a functional covariate X that takes values in an infinite dimensional space. The main purpose is to introduce a kernel-type estimator of the conditional geometric quantiles whenever functional
stationary ergodic data are considered.We established the strong consistency with rate of the proposed estimator and gave an application to joint horizon time series forecasting

This paper, investigates the conditional quantile estimation of a scalar random response and a functional random covariate (i.e. valued in some infinite-dimensional space) whenever functional stationary ergodic data with random censorship are considered. We introduce a kernel type estimator of the conditional quantile function. We establish the strong consistency with rate of this estimator as well as the asymptotic normality which induces a confidence interval that is usable in practice since it does not depend on any unknown quantity. An application to electricity peak demand interval prediction with censored smart meter data is carried out to show the performance of the proposed estimator.

Energy suppliers are facing ever increasing competition, so that factors like quality and continuity of offered services must be properly taken into account. Furthermore, in the last few years, many countries are interested in renewable energies such as solar and wind. Renewable energy resources are mainly used for environmental and economic reasons such as reducing the carbon emission. It might also be used to reinforce the electric network especially during high peak periods. However, the injection of such energy resources in the low-voltage (LV) network can leads to high voltage constrains. To overcome this issue, one can motivate customers to use thermal or electric storage devices during high-production periods of PV to foster the integration of renewable energy generation into the network. In this paper, we are interested in forecasting household-level electricity demand which represents a key factor to assure the balance supply/demand in the LV network. A novel methodology able to improve short term functional time series forecasts has been introduced. An application to the Irish smart meter data set showed the performance of the proposed methodology to forecast the intra-day household level load curves.

In this paper, a nonparametric estimator is proposed for estimating the L1-median for multi- variate conditional distribution when the covariates take values in an infinite dimensional space. The multivariate case is more appropriate to predict the components of a vector of random variables simultaneously rather than predicting each of them separately. While estimating the conditional L1-median function using the well-known Nadarya-Waston estimator, we establish the strong consistency of this estimator as well as the asymptotic normality. We also present some simulations and provide how to built conditional confidence ellipsoids for the multivariate L1-median regression in practice. Some numerical study in chemiometrical real data are car- ried out to compare the multivariate L1-median regression with the vector of marginal median regression when the covariate X is a curve as well as X is a random vector.

We propose a very simple algorithm in order to estimate the geometric median, also called spatial median, of multivariate (Small, 1990) or functional data (Gervini, 2008) when the sample size is large. A simple and fast iterative approach based on the Robbins-Monro algorithm (Duflo, 1997) as well as its averaged version (Polyak and Juditsky, 1992) are shown to be effective for large samples of high dimension data. They are very fast and only require O(Nd) elementary operations, where N is the sample size and d is the dimension of data. The averaged approach is shown to be more effective and less sensitive to the tuning parameter. The ability of this new estimator to estimate accurately and rapidly (about thirty times faster than the classical estimator) the geometric median is illustrated on a large sample of 18902 electricity consumption curves measured every half an hour during one week.

This work aims at performing functional principal components analysis (FPCA) with Horvitz– Thompson estimators when the observations are curves collected with survey sampling tech- niques. One important motivation for this study is that FPCA is a dimension reduction tool which is the first step to develop model-assisted approaches that can take auxiliary infor- mation into account. FPCA relies on the estimation of the eigenelements of the covariance operator which can be seen as nonlinear functionals. Adapting to our functional context the linearization technique based on the influence function developed by Deville [1999. Variance estimation for complex statistics and estimators: linearization and residual techniques. Survey Methodology 25, 193–203], we prove that these estimators are asymptotically design unbi- ased and consistent. Under mild assumptions, asymptotic variances are derived for the FPCA' estimators and consistent estimators of them are proposed. Our approach is illustrated with a simulation study and we check the good properties of the proposed estimators of the eigenele- ments as well as their variance estimators obtained with the linearization approach.

Geometric quantiles are investigated using data collected from a complex survey. Geometric quantiles are an extension of univariate quantiles in a multivariate set-up that uses the geometry of multivariate data clouds. A very important application of geometric quantiles is the detection of outliers in multivariate data by means of quantile contours. A design-based estimator of geometric quantiles is constructed and used to compute quantile contours in order to detect outliers in both multivariate data and survey sampling set-ups. An algorithm for computing geometric quantile estimates is also developed. Under broad assumptions, the asymptotic variance of the quantile estimator is derived and a consistent variance estimator is proposed. Theoretical results are illustrated with simulated and real data.

The present paper deals with a nonparametric M-estimation for right censored regression model with stationary ergodic data. Defined as an implicit function, a kernel type estimator of a family of robust regression is considered when the covariate take its values in R d (d ≥ 1) and the data are sampled from stationary ergodic process. The strong consistency (with rate) and the asymptotic distribution of the estimator are established under mild assumptions. Moreover, a usable confidence interval is provided which does not depend on any unknown quantity. Our results hold without any mixing condition and do not require the existence of marginal densities. A comparison study based on simulated data is also provided.