L'objectif de cette thèse est d'appliquer les méthodes d'approximations stochastiques à l'estimation de la densité et de la régression. Dans le premier chapitre, nous construisons un algorithme stochastique à pas simple qui définit toute une famille d'estimateurs récursifs à noyau d'une densité de probabilité. Nous étudions les différentes propriétés de cet algorithme. En particulier, nous identifions deux classes d'estimateurs; la première correspond à un choix de pas qui permet d'obtenir un risque minimal, la seconde une variance minimale. Dans le deuxième chapitre, nous nous intéressons à l'estimateur proposé par Révész (1973, 1977) pour estimer une fonction de régression r:x-> E[Y|X=x]. Son estimateur r_n, construit à l'aide d'un algorithme stochastique à pas simple, a un gros inconvénient: les hypothèses sur la densité marginale de X nécessaires pour établir la vitesse de convergence de r_n sont beaucoup plus fortes que celles habituellement requises pour étudier le comportement asymptotique d'un estimateur d'une fonction de régression. Nous montrons comment l'application du principe de moyennisation des algorithmes stochastiques permet, tout d'abord en généralisant la définition de l'estimateur de Révész, puis en moyennisant cet estimateur généralisé, de construire un estimateur récursif br_n qui possède de bonnes propriétés asymptotiques. Dans le troisième chapitre, nous appliquons à nouveau les méthodes d'approximation stochastique à l'estimation d'une fonction de régression. Mais cette fois, plutôt que d'utiliser des algorithmes stochastiques à pas simple, nous montrons comment les algorithmes stochastiques à pas doubles permettent de construire toute une classe d'estimateurs récursifs d'une fonction de régression, et nous étudions les propriétés asymptotiques de ces estimateurs. Cette approche est beaucoup plus simple que celle du deuxième chapitre: les estimateurs construits à l'aide des algorithmes à pas doubles n'ont pas besoin d'être moyennisés pour avoir les bonnes propriétés asymptotiques.

La vraisemblance empirique est une méthode d'estimation inspirée de la vraisemblance classique, mais s'affranchissant du choix d'une famille paramétrique de lois. Cette méthode semi-paramétrique consiste à maximiser la vraisemblance d'une loi ne chargeant que les données et permet de construire des régions de confiance lorsque le paramètre d'intérêt est défini à partir de contraintes de moments.<br />Dans cette thèse, nous généraliserons la méthode de vraisemblance empirique à une vaste gamme de méthodes de divergence empirique. Nous montrerons que l'on peut obtenir des résultats non asymptotiques originaux pour certaines divergences. Nous proposerons également une adaptation de la vraisemblance empirique aux chaînes de Markov. Nous mènerons deux applications : l'estimation d'un indice du risque d'exposition au méthylmercure, en combinant les diverses sources de données disponibles, et l'étude du rôle de la norme sociale sur le surpoids et l'obésité.

Dans cette thèse, on étudie certaines propriétés asymptotiques d'un modèle de polymère dirigé en milieu aléatoire. Plus précisément, on étudie les liens entre la fonction de partition et la mesure de polymère lorsque la taille du système tend vers l'infini. On construit également des champs multifractaux qui vérifient certaines propriétés statistiques du champ de vitesse d'un écoulement turbulent.

Thesis (Ed. D.)--West Virginia University, 2002. / Title from document title page. Document formatted into pages; contains ix, 106 p. : ill. Includes abstract. Includes bibliographical references (p. 76-82).

In most high school curriculum Science Technology, Engineering and Mathematics (STEM) classes are taught separately but there is increased attention and funding for STEM integration. This paper examines the history of why high schools teach STEM courses separately, how classrooms and curriculum can be integrated, and the benefits and challenges associated with STEM integration. A tool for evaluating integrated units is included with the analysis of a current integrated high school project used in a Precalculus and Scientific Research and Design course taught at a high school. / text

This study examines the impact of the municipality level characteristics on the average Math achievement of students in third year of lower secondary schools in Mexico. Using data from different Mexican and international sources and multi-level regression models the present work shows that municipality characteristics provide additional explanation of the unexplained variability in educational achievement controlling for school-level factors and even without accounting for student characteristics. Although school factors are highly correlated with municipality’s characteristics, the present study finds that unobservable characteristics of the municipality are playing an important role in Mexican students’ achievement which goes beyond the possible impact that school factors have on achievement. / text

This exploratory study investigated the techniques used by teachers of the visually impaired when administering math questions with graphics to students with blindness or low vision. The researcher observed and videotaped 10 pairs of students with visual impairments and their teachers while the students were taking a test that consisted of 12 graphic math items and found a wide variance existed between teachers in the administering of mathematical test items with graphics to their students. The most prevalent teacher behaviors observed were teacher initiation and graph detail description. For the majority of the teacher initiated responses, teachers gave information on a specific detail of the math graphic. Students predominantly asked for clarification regarding the math graphic itself or clarification of the math problem itself. Teachers used a variety of factors in determining if and when students required assistance during testing for large print or tactile graphics. No statistical significance was found between braille and large print groups with regard to teacher variation, student variation, and scores on test items, No relationship was found between correct answers on the test and teacher variation scores but a strong, positive correlation existed for total test time and teacher variation scores. In addition, there was no statistical significance, between the six math graph types used in this study. Hand movements of braille students were also observed, 90% of students using either both hands or mostly both hands when exploring the tactile graphic math problem. A horizontal movement was the primary direction students used when examining the tactile graphic. Recommendations were made regarding future research with large print and tactile graphics

Math difficulties (MD) are nearly as common as difficulties with reading. Despite this, MDs have received much less attention from researchers and we have yet to define a core cognitive process for MD. Knowledge about a core cognitive process would assist with early identification and remediation of MDs. Working memory has been identified as one cognitive process that is strongly associated with math difficulties. Most research examining the association between working memory and math calculation skills has been predicated on Baddeley and Hitch’s (1974) multicomponent model of working memory. Results of studies are inconclusive with respect to which component of Baddeley and Hitch’s model is most associated with math calculation skills. The wide variety of tasks that have been used to measure the components of Baddeley and Hitch’s model may be one reason for the lack of consistent findings. In the Introduction, common tasks used to measure the components of Baddeley and Hitch’s model are described and discussed. The Automated Working Memory Assessment Battery (AWMA) is suggested as a measure that adequately assesses all components of Baddeley and Hitch’s model. The AWMA was used in two studies examining the role of the components of working memory in math calculation skill in elementary-school (Study 1) and university (Study 2) students. Participants in Study 1were 94 (42 female) elementary-school children (M age = 9 years 1 month; Range 6 years 0 months – 11 years 8 months). Participants in Study 2 were 42 university students (M age 20 years 9 months; Range 18 years 6 months to 22 years 11 months). In both studies, the visuospatial sketchpad (short-term visuospatial memory) emerged as the component of working memory that explained the most variance in math calculation scores. In elementary-school children, phonological processing was also important. Evidence points to a developmental path emphasizing both verbal and visuospatial skills in math calculation skills of younger children and a more specific role for visuospatial memory in adults (university students). Explicit instruction using visuospatial strategies in the teaching of math calculation skills will be important at all ages.

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Math anxiety is a greatly understudied construct in children. In adult and adolescent samples, research shows that a number of factors are related to math anxiety including negative self-perceptions and outcomes. It is unknown if these same factors are related to math anxiety in children. This study was conducted to identify factors related to math anxiety in second grade children. Using Bandura's (1989) theory of triadic reciprocity as a theoretical model, children (n=91) and their parents (n=81) completed a series of self-report measures on math anxiety, math self-concept, reading self-concept, math self-efficacy, and aspects of the home math environment. Results indicated that the strongest predictor of math anxiety in second grade children was their level of math self-concept. The addition of environmental factors did not significantly increase the amount variance explained in math anxiety. Furthermore, despite research with adults that shows strong gender differences in math anxiety, no gender differences in math anxiety were found in second grade children. The discussion focuses on possible explanations for these findings as well as directions for future research. / Department of Educational Psychology