L’objectif de cette thèse CIFRE, réalisée avec la société d’études de marché BVA en collaboration avec le constructeur automobile Renault, est de mesurer l’impact des investissements media pour différents canaux (télévision, affichage, etc.) sur les parts de marché de différentes marques, en prenant en compte la concurrence et les potentiels effets croisés et synergies entre ces marques, ainsi qu’en tenant compte du prix des véhicules, du contexte réglementaire (i.e. prime à la casse), et des effets retard de la publicité.Nous avons puisé dans les littératures marketing et statistique pour développer, comparer et interpréter plusieurs modèles qui respectent la contrainte de somme unitaire des parts de marché. Une application concrète au marché automobile français est présentée, pour laquelle nous montrons que les parts de marché des marques sont plus ou moins sensibles aux investissements publicitaires consentis dans chaque canal, et qu’il existe de synergies entre certaines marques. / The aim of this CIFRE thesis, realized with the market research institute BVA in collaboration with the automobile manufacturer Renault, is to build a model in order to measure the impact of media investments of several channels (television, outdoor, etc.) on the brands’ market shares, taking into account the competition and the potential cross effects and synergies between brands, as well as accounting for the price, the regulatory context (scrapping incentive), and the lagged effects of advertising. We have drawn from marketing and statistical literatures to develop, compare and interpret several models which respect the unit sum constraint of market shares. A practical application to the French automobile market is presented, for which it is shown that brands’ market shares are more or less sensitive to advertising investments made in each channel, and that synergies between brands exist.

This study investigated the discrimination between sources of the semi-precious mineral, nephrite, by a targeted microanalytical determination of the elemental composition, including the trace elements. Nephrite specimens were collected from two significant nephrite sources in New Zealand, namely the Westland and Wakatipu fields, and combined with donated specimens from the Southland field to complete a representative collection of New Zealand nephrite. A small number of nephrite specimens were donated from the South Westland nephrite field and from foreign sources. Representative fragments of these specimens were analysed by electron microprobe analysis (EMPA) for major elements and by laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) for trace elements. The data obtained by the analytical procedure were treated within a compositional data (CoDa) framework of statistical analysis that focuses on the relative sizes of the components in the data set. The data were transformed under the guidelines of the CoDa framework, where appropriate, and the transformed data were treated with standard statistical methods for exploratory data analysis, dimension reduction and discriminant analysis. Advances were made to the Hotelling’s method for comparison of multivariate means by incorporating a permutation evaluation step. This permutation method removes the requirement for multivariate normality, and it also allows comparisons to be made when there are many more variables than observations, as is often the case when objects are being characterized using elemental data. The strategy used in this study showed that it is possible to discriminate between sources of nephrite at both an intra- and inter-source level within New Zealand. In addition, an exploratory investigation showed that New Zealand nephrite could be differentiated from the few nephrite specimens from foreign sources that were available for comparison. Recommendations are made for the protection of the New Zealand nephrite resource and for casework, based on the results obtained in this study.

This study investigated the discrimination between sources of the semi-precious mineral, nephrite, by a targeted microanalytical determination of the elemental composition, including the trace elements. Nephrite specimens were collected from two significant nephrite sources in New Zealand, namely the Westland and Wakatipu fields, and combined with donated specimens from the Southland field to complete a representative collection of New Zealand nephrite. A small number of nephrite specimens were donated from the South Westland nephrite field and from foreign sources. Representative fragments of these specimens were analysed by electron microprobe analysis (EMPA) for major elements and by laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) for trace elements. The data obtained by the analytical procedure were treated within a compositional data (CoDa) framework of statistical analysis that focuses on the relative sizes of the components in the data set. The data were transformed under the guidelines of the CoDa framework, where appropriate, and the transformed data were treated with standard statistical methods for exploratory data analysis, dimension reduction and discriminant analysis. Advances were made to the Hotelling’s method for comparison of multivariate means by incorporating a permutation evaluation step. This permutation method removes the requirement for multivariate normality, and it also allows comparisons to be made when there are many more variables than observations, as is often the case when objects are being characterized using elemental data. The strategy used in this study showed that it is possible to discriminate between sources of nephrite at both an intra- and inter-source level within New Zealand. In addition, an exploratory investigation showed that New Zealand nephrite could be differentiated from the few nephrite specimens from foreign sources that were available for comparison. Recommendations are made for the protection of the New Zealand nephrite resource and for casework, based on the results obtained in this study.

This study investigated the discrimination between sources of the semi-precious mineral, nephrite, by a targeted microanalytical determination of the elemental composition, including the trace elements. Nephrite specimens were collected from two significant nephrite sources in New Zealand, namely the Westland and Wakatipu fields, and combined with donated specimens from the Southland field to complete a representative collection of New Zealand nephrite. A small number of nephrite specimens were donated from the South Westland nephrite field and from foreign sources. Representative fragments of these specimens were analysed by electron microprobe analysis (EMPA) for major elements and by laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) for trace elements. The data obtained by the analytical procedure were treated within a compositional data (CoDa) framework of statistical analysis that focuses on the relative sizes of the components in the data set. The data were transformed under the guidelines of the CoDa framework, where appropriate, and the transformed data were treated with standard statistical methods for exploratory data analysis, dimension reduction and discriminant analysis. Advances were made to the Hotelling’s method for comparison of multivariate means by incorporating a permutation evaluation step. This permutation method removes the requirement for multivariate normality, and it also allows comparisons to be made when there are many more variables than observations, as is often the case when objects are being characterized using elemental data. The strategy used in this study showed that it is possible to discriminate between sources of nephrite at both an intra- and inter-source level within New Zealand. In addition, an exploratory investigation showed that New Zealand nephrite could be differentiated from the few nephrite specimens from foreign sources that were available for comparison. Recommendations are made for the protection of the New Zealand nephrite resource and for casework, based on the results obtained in this study.

This study investigated the discrimination between sources of the semi-precious mineral, nephrite, by a targeted microanalytical determination of the elemental composition, including the trace elements. Nephrite specimens were collected from two significant nephrite sources in New Zealand, namely the Westland and Wakatipu fields, and combined with donated specimens from the Southland field to complete a representative collection of New Zealand nephrite. A small number of nephrite specimens were donated from the South Westland nephrite field and from foreign sources. Representative fragments of these specimens were analysed by electron microprobe analysis (EMPA) for major elements and by laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) for trace elements. The data obtained by the analytical procedure were treated within a compositional data (CoDa) framework of statistical analysis that focuses on the relative sizes of the components in the data set. The data were transformed under the guidelines of the CoDa framework, where appropriate, and the transformed data were treated with standard statistical methods for exploratory data analysis, dimension reduction and discriminant analysis. Advances were made to the Hotelling’s method for comparison of multivariate means by incorporating a permutation evaluation step. This permutation method removes the requirement for multivariate normality, and it also allows comparisons to be made when there are many more variables than observations, as is often the case when objects are being characterized using elemental data. The strategy used in this study showed that it is possible to discriminate between sources of nephrite at both an intra- and inter-source level within New Zealand. In addition, an exploratory investigation showed that New Zealand nephrite could be differentiated from the few nephrite specimens from foreign sources that were available for comparison. Recommendations are made for the protection of the New Zealand nephrite resource and for casework, based on the results obtained in this study.

Compositional data, where measurements are vectors with each component constituting a percentage of a whole, is abundant throughout many disciplines of science. Consequently, there is a strong need to establish valid statistical procedures for this type of data. In this work the basic theory of the compositional sample space is presented and through simulation studies and a case study on data from industrial applications, the current available methods for regression as applied to compositional data are evaluated. The main focus of this work is to establish linear regression in a way compatible with compositional data sets and compare this approach with the alternative of applying standard multivariate regression methods on raw compositional data. It is found that for several data sets, the difference between 'naive' multivariate linear regression and compositional linear regression is negligible; while for others (in particular where the dependence of covariates is not strictly linear) the compositional regression methods are shown to be stronger.

Dados composicionais são constituídos por vetores cujas componentes representam as proporções de algum montante, isto é: vetores com entradas positivas cuja soma é igual a 1. Em diversas áreas do conhecimento, o problema de estimar as partes $y_1, y_2, \\dots, y_D$ correspondentes aos setores $SE_1, SE_2, \\dots, SE_D$, de uma certa quantidade $Q$, aparece com frequência. As porcentagens $y_1, y_2, \\dots, y_D$ de intenção de votos correspondentes aos candidatos $Ca_1, Ca_2, \\dots, Ca_D$ em eleições governamentais ou as parcelas de mercado correspondentes a industrias concorrentes formam exemplos típicos. Naturalmente, é de grande interesse analisar como variam tais proporções em função de certas mudanças contextuais, por exemplo, a localização geográfica ou o tempo. Em qualquer ambiente competitivo, informações sobre esse comportamento são de grande auxílio para a elaboração das estratégias dos concorrentes. Neste trabalho, apresentamos e discutimos algumas abordagens propostas na literatura para regressão sobre dados composicionais, assim como alguns métodos de seleção de modelos baseados em inferência bayesiana. \\\\ / Compositional data consist of vectors whose components are the proportions of some whole. The problem of estimating the portions $y_1, y_2, \\dots, y_D$ corresponding to the pieces $SE_1, SE_2, \\dots, SE_D$ of some whole $Q$ is often required in several domains of knowledge. The percentages $y_1, y_2, \\dots, y_D$ of votes corresponding to the competitors $Ca_1, Ca_2, \\dots, Ca_D$ in governmental elections or market share problems are typical examples. Of course, it is of great interest to study the behavior of such proportions according to some contextual transitions. In any competitive environmet, additional information of such behavior can be very helpful for the strategists to make proper decisions. In this work we present and discuss some approaches proposed by different authors for compositional data regression as well as some model selection methods based on bayesian inference.\\\\

Variations in predator diets is important in ecology to help us understand their top-down effects on the ecosystem. In predator diets, their fatty acid signatures reflect the proportions of prey consumed. Since fatty acid signatures are compositional and often longer than the sample size, a standard MANOVA test is unsuitable. Here, non-parametric MANOVA techniques are developed to test for differences in fatty acid signatures among locations, years, and seasons which infer differences in diets. Simulations show that the test has good power and appropriate type I error rates. The tests developed were applied to data on Greenland Sharks to test for differences in diets between individuals from Cumberland Sound, Canada, versus those from Svalbard, Norway and whether there is a yearly and/or seasonal effect on the diets. Diet compositions were found to vary between the locations, seasons and years, possibly caused by differing prey species distributions, migrations, and climate change.

Dados composicionais são constituídos por vetores cujas componentes representam as proporções de algum montante, isto é: vetores com entradas positivas cuja soma é igual a 1. Em diversas áreas do conhecimento, o problema de estimar as partes $y_1, y_2, \\dots, y_D$ correspondentes aos setores $SE_1, SE_2, \\dots, SE_D$, de uma certa quantidade $Q$, aparece com frequência. As porcentagens $y_1, y_2, \\dots, y_D$ de intenção de votos correspondentes aos candidatos $Ca_1, Ca_2, \\dots, Ca_D$ em eleições governamentais ou as parcelas de mercado correspondentes a industrias concorrentes formam exemplos típicos. Naturalmente, é de grande interesse analisar como variam tais proporções em função de certas mudanças contextuais, por exemplo, a localização geográfica ou o tempo. Em qualquer ambiente competitivo, informações sobre esse comportamento são de grande auxílio para a elaboração das estratégias dos concorrentes. Neste trabalho, apresentamos e discutimos algumas abordagens propostas na literatura para regressão sobre dados composicionais, assim como alguns métodos de seleção de modelos baseados em inferência bayesiana. \\\\ / Compositional data consist of vectors whose components are the proportions of some whole. The problem of estimating the portions $y_1, y_2, \\dots, y_D$ corresponding to the pieces $SE_1, SE_2, \\dots, SE_D$ of some whole $Q$ is often required in several domains of knowledge. The percentages $y_1, y_2, \\dots, y_D$ of votes corresponding to the competitors $Ca_1, Ca_2, \\dots, Ca_D$ in governmental elections or market share problems are typical examples. Of course, it is of great interest to study the behavior of such proportions according to some contextual transitions. In any competitive environmet, additional information of such behavior can be very helpful for the strategists to make proper decisions. In this work we present and discuss some approaches proposed by different authors for compositional data regression as well as some model selection methods based on bayesian inference.\\\\

Microbiome research has become a ubiquitous component of contemporary clinical research, with potential to uncover associations between microbiome composition and disease. With microbiome data becoming more prevalent, the need to understand how to analyse such data is increasingly important. One complicating property of microbiome data is that it is inherently compositional and thus constrained to simplex-space; because of this, it cannot be analysed directly using conventional statistical methods. In this paper, we transform the compositional data in order to lift the simplex-constraint, and then investigate the viability of applying conventional statistical methods to the data. Using a high-dimensional data set containing gut-microbiome samples from Parkinson's- and control patients, we first transform the raw data to centred log-ratio scale, and then use permutational multivariate analysis of variance (PERMANOVA) to test if there are differences between the two groups with respect to bacterial abundances. We then employ three machine learning classifiers -- Logistic regression, XGBoost, and Random Forest -- and evaluate their performance on the transformed data. The results from PERMANOVA indicate that gut-microbiome composition in the patients with Parkinson's disease indeed differ from that in the control individuals. The Random Forest method achieves the highest classification accuracy, followed by XGBoost, while logistic regression performs poorly, questioning its viability in analysis of high-dimensional compositional microbiome data. We find four bacterial species of high importance for the classification: Prevotella copri, Prevotella sp. CAG 520, Akkermansia muciniphila, and Butyricimonas virosa, where the first three have been previously mentioned in the Parkinson's literature.