Design of experiment (DOE) is a statistical method for testing effects of input factors into a process based on its responses or outputs. Since the influence of these factors and their interactions are studied from the process outputs, then quality of these outputs or the measurements play a significant role in a correct statistical conclusion about the significance of factors and their interactions. Linear regression is a method, which can be applied for the DOE purpose, the parameters of such a regression model are estimated by the ordinary least-squares (OLS) method. This method is sensitive to the presence of any blunder in measurements, meaning that blunders significantly affect the result of a regression using OLS method. This research aims to perform a robustness analysis for some full factorial DOEs by different robust estimators as well as the Taguchi methodology. A full factorial DOE with three factors at three levels, two replicants, and three replicants are performed is studied. Taguchi's approach is conducted by computing the signal-to-noise ratio (S/N) from three replicants, where the lower noise factor means the stronger signal. Robust estimators of Andrews, Cauchy, Fair, Huber, Logistic, Talwar, and Welsch are applied to the DOE in different setups and adding different types and percentages of blunders or gross errors to the data to assess the success rate of each. Number and size of the blunders in the measurements are two important factors influencing the success rate of a robust estimator. For evaluation, our measurements are infected by blunders up to different percentages of data. Our study showed the Talwar robust estimator is the best amongst the rest of estimators and resists well against up to 80% of presence of blunders. Consequently, the use of this estimator instated of the OLS is recommended for DOE purposes. The comparison between Taguchi’s method and robust estimators showed that blunders affect the signal-to-noise ratio as the signal is significantly changed by them, whilst robust estimators suppress the blunders well and the same conclusion as that with the OLS with no blunder can be drawn from them.

Le développement des approches robustes et non paramétriques pour l’analyse et le traitement statistique de gros volumes de données présentant une forte variabilité,comme dans les domaines de l’environnement et de la génétique, est fondamental.Nous modélisons ici des données complexes de biologie appliquées à l’étude du comportement de bivalves et à l’analyse de liaison génétique. L’application des mathématiques à l’analyse du comportement de mollusques bivalves nous a permis d’aller vers une quantification et une traduction mathématique de comportements d’animaux in-situ, en milieu proche ou lointain. Nous avons proposé un modèle de régression non paramétrique et comparé 3 estimateurs non paramétriques, récursifs ou non,de la fonction de régression pour optimiser le meilleur estimateur. Nous avons ensuite caractérisé des rythmes biologiques, formalisé l’évolution d’états d’ouvertures,proposé des méthodes de discrimination de comportements, utilisé la méthode des shot-noises pour caractériser différents états d’ouverture-fermetures transitoires et développé une méthode originale de mesure de croissance en ligne.En génétique, nous avons abordé un cadre plus général de statistiques robustes pour l’analyse de liaison génétique. Nous avons développé des estimateurs robustes aux hypothèses de normalités et à la présence de valeurs aberrantes, nous avons aussi utilisé une approche statistique, où nous avons abordé la dépendance entre variables aléatoires via la théorie des copules. Nos principaux résultats ont montré l’intérêt pratique de ces estimateurs sur des données réelles de QTL et eQTL. / The development of robust and nonparametric approaches for the analysis and statistical treatment of high-dimensional data sets exhibiting high variability, as seen in the environmental and genetic fields, is instrumental. Here, we model complex biological data with application to the analysis of bivalves’ behavior and to linkage analysis. The application of mathematics to the analysis of mollusk bivalves’behavior gave us the possibility to quantify and translate mathematically the animals’behavior in situ, in close or far field. We proposed a nonparametric regression model and compared three nonparametric estimators (recursive or not) of the regressionfunction to optimize the best estimator. We then characterized the biological rhythms, formalized the states of opening, proposed methods able to discriminate the behaviors, used shot-noise analysis to characterize various opening/closing transitory states and developed an original approach for measuring online growth.In genetics, we proposed a more general framework of robust statistics for linkage analysis. We developed estimators robust to distribution assumptions and the presence of outlier observations. We also used a statistical approach where the dependence between random variables is specified through copula theory. Our main results showed the practical interest of these estimators on real data for QTL and eQTL analysis.

The aim of this thesis is to describe and further develop estimation strategies for data obtained by stratified sampling. Estimation of the mean and linear regression model are discussed. The possible inclusion of auxiliary variables in the estimation is exam- ined. The auxiliary variables can be transformed rather than used in their original form. A transformation minimizing the asymptotic variance of the resulting estimator is pro- vided. The estimator using an approach from this thesis is compared to the doubly robust estimator and shown to be asymptotically equivalent.

This thesis if focused on the application of methods of robust econometrics to real economic data. We focuse on the issuies of international trade in Czech Republic and the problem of employment and growth of small businesses in Europe. We also focues on estimation of panel data by classical approaches (least squares, fixed effects, GMM) and bzy robust techniques. The first part of dissertation focuses on analyzing determinants of FDI in Czech manufacturing industry. The aim is to estimate a model where the stock of FDI is expressed as a function of several economic factors (K/L, profit per worker, R&D, Balassa index and others). We estimate these models by OLS, fixed effects and GMM. With regard to ambiguous results we used least trimmed squares as a diagnostic tool for detection of outliers. Elimination of two polluting industries out of the data set brings certain improvement in significance of some factors. The second part of dissertation we focus on an estimation of models of employment and net production in 28 European countries for small businesses as a function of economic and institutional variables by special technique of estimation. We describe robust version of within group fixed effects estimation. The aim of paper is to estimate a set of models and to test the properties of estimator. With...