The growth in the use of machine learning in different areas has revealed challenging classification problems that require robust systems. Multiple Classier Systems (MCSs) have attracted interest from researchers as a method that could address such problems. Optimizing the fitness of an MCS improves its, robustness. The lack of an analysis for MCSs from a fitness perspective is identified. To fill this gap, an analytic model from this perspective is derived mathematically by extending the error analysis introduced by Brown and Kuncheva in 2010. The model relates the fitness of an MCS to the average accuracy, positive-diversity, and negative-diversity of the classifiers that constitute the MCS. The model is verified using a statistical analysis of a Monte-Carlo based simulation. This shows the significance of the indicated relationships by the model. This model provides guidelines for developing robust MCSs. It enables the selection of classifiers which compose an MCS with an improved fitness while improving computational cost by avoiding local calculations. The usefulness of the model for designing classification systems is investigated. A new measure consisting of the accuracy and positive-diversity is developed. This measure evaluates fitness while avoiding many calculations compared to the regular measures. A new system (Gadapt) is developed. Gadapt combines machine learning and genetic algorithms to define subsets of the feature space that closely match true class regions. It uses the new measure as a multi-objective criterion for a multi-objective genetic algorithm to identify the MCSs those create the subsets. The design of Gadapt is validated experimentally. The usefulness of the measure and the method of determining the subsets for the performance of Gadapt are examined based on five generated data sets that represent a wide range of problems. The robustness of Gadapt to small amounts of training data is evaluated in comparison with five existing systems on four benchmark data sets. The performance of Gadapt is evaluated in comparison with eleven existing systems on nine benchmark data sets. The analysis of the experiment results supports the validity of the Gadapt design and the outperforming of Gadapt on the existing systems in terms of robustness and performance.

This thesis shows how to test the fit of a data set to a number of different models, using Watson’s U2 statistic for both grouped and continuous data. While Watson’s U2 statistic was introduced for continuous data, in recent work, the statistic has been adapted for grouped data. However, when using Watson’s U2 for continuous data, the asymptotic distribution is difficult to obtain, particularly, for some skewed circular distributions that contain four or five parameters. Until now, U2 asymptotic points are worked out only for uniform distribution and the von Mises distribution among all circular distributions. We give U2 asymptotic points for the wrapped exponential distributions, and we show that U2 asymptotic points when data are grouped is usually easier to obtain for other more advanced circular distributions. In practice, all continuous data is grouped into cells whose width is decided by the accuracy of the measurement. It will be found useful to treat such data as grouped with sufficient number of cells in the examples to be analyzed. When the data are treated as grouped, asymptotic points for U2 match well with the points when the data are treated as continuous. Asymptotic theory for U2 adopted for grouped data is given in the thesis. Monte Carlo studies show that, for reasonable sample sizes, the asymptotic points will give good approximations to the p-values of the test.

Thesis (Ph.D.)--Mississippi State University. Department of Mathematics and Statistics. / Title from title screen. Includes bibliographical references.

Goodness-of-fit tests have been studied by many researchers. Among them, an alternative statistical test for uniformity was proposed by Chen and Ye (2009). The test was used by Xiong (2010) to test normality for the case that both location parameter and scale parameter of the normal distribution are known. The purpose of the present thesis is to extend the result to the case that the parameters are unknown. A table for the critical values of the test statistic is obtained using Monte Carlo simulation. The performance of the proposed test is compared with the Shapiro-Wilk test and the Kolmogorov-Smirnov test. Monte-Carlo simulation results show that proposed test performs better than the Kolmogorov-Smirnov test in many cases. The Shapiro Wilk test is still the most powerful test although in some cases the test proposed in the present research performs better.

De nos jours, on assiste à l'émergence massive de nouveaux systèmes électroniques exploitant des fréquences de plus en plus élevées, particulièrement en ondes millimétriques (30-300 GHz). Il apparaît de ce fait un besoin potentiel de développement de nouveaux moyens d'essai appropriés dans le domaine millimétrique. En particulier, l'étude de la biocompatibilité de ces systèmes est clairement identifiée comme une priorité de recherche en électromagnétisme. Dans ce contexte, l'objectif de cette thèse consiste à concevoir et à évaluer les propriétés d'une chambre réverbérante à brassage de modes (CRBM) en bande Ka (26,5-40 GHz), en bande U (40-60 GHz) et en bande V (50-75 GHz). L'application visée dans cette thèse concerne la mise en place d'outils dosimétriques par caméra infrarouge en chambre réverbérante et la réalisation d'essais préliminaires sur des fantômes diélectriques à 60 GHz. Dans un premier temps, nous avons analysé numériquement le comportement statistique du champ électrique dans une cavité pré-dimensionnée. Les simulations sont réalisées à l'aide d'un outil interne de modélisation du comportement d'une CRBM basé sur la théorie des images. A l'aide du test d'ajustement statistique d'Anderson-Darling, nous avons montré que le comportement de la chambre en ondes millimétriques est en adéquation avec le modèle de Hill (champ statistiquement homogène et isotrope dans le volume de l'enceinte) . Dans un second temps, nous avons réalisé un prototype de chambre réverbérante de dimensions internes : 42,3 x 41,2 x 38,3 cm3 . Un processus de brassage par saut de fréquence est utilisé pour l'obtention de l'uniformité statistique de la densité de puissance. La chambre est équipée d'un système de positionnement fin et précis permettant l'échantillonnage spatial de la puissance sur un axe à l'intérieur de la chambre. Les accès millimétriques ont également été étudiés de sorte à réduire d'éventuelles fuites significatives. Les liaisons entre la source millimétrique et l'antenne d'émission d'une part et celles entre l'antenne de réception et l'analyseur de spectre d'autre part sont assurées par des guides d'onde. Nous avons également mis en place l'ensemble des équipements nécessaires pour le fonctionnement de la chambre (source, analyseur de spectre, mélangeur). La chambre est caractérisée dans la bande 58,5-61,5 GHz. Les résultats obtenus sont satisfaisants en termes de coefficient de qualité et de comportement statistique de la puissance mesurée dans un volume de test donné. Dans un troisième temps, nous avons modélisé puis réalisé une interface intégrée sur une des parois de la chambre pour la mesure de température par caméra infrarouge. Des mesures préliminaires sont réalisées sur un fantôme constitué essentiellement d'eau. Les résultats expérimentaux et théoriques de l'évaluation du gradient de la température sur le fantôme sont très proches. Ceci confirme que la chambre réverbérante ainsi conçue permet de soumettre l'objet sous test à une illumination statistiquement uniforme et calibrée en puissance. Un tel dispositif est un atout précieux pour des tests de compatibilité électromagnétique d'équipements électroniques dans la bande 26,5-75 GHz. Cette CRBM pourrait également permettre de réal iser des essais préliminaires dans le cadre de l'étude des interactions des ondes avec la matière vivante en millimétrique. / Nowadays, there is a massive emergence of new electronic systems operating at increasing frequencies, especially in the millimeter waves range (30-300 GHz). As a consequence, development of new appropriate test facilities in the millimeter waves range is needed. ln particular, the study of the biocompatibility of the se systems is cie arly identified as a research priority in electromagnetism. ln this context, this thesis deals with the design and the evaluation of a modestirred reverberation chamber (RC) properties in the Ka band (26.5-40 GHz), U band (40-60 GHz) and V band (50-75 GHz). The intended application in this thesis concerns the development of a dosimetric tool using an infrared camera in a reverberation chamber. Firstly, we numerically analyze the statistical behavior of the electric field in the test volume of such an RC. A numerical model based on image theory is used to simulate the cavity. With Anderson-Darling goodness-of-fit test, we show !hat the chamber behaves very weil at millimeter waves frequency in terms of statistical distribution of the field in the test volume. Secondly, a compact reverberation chamber is designed and built up, with the following internai dimensions 42.3 x 41.2 x 38.3 cm3 . The statistical uniformity of power density in the chamber volume is obtained by frequency stirring. The RC is associated with a positioning system for spatial sampling of power inside reverberation chamber. The interfaces are also studied in order to reduce any significant leakage. Waveguides are used in the transmission and reception chains to minimize losses. We have also set up ali the equipment necessary for carrying out measurements (source, spectrum analyzer, mixer). The RC is characterized in the 58.5-61.5 GHz range. The results are satisfactory in terms of the quality factor level and the statistical distribution of the power in the test volume. Thirdly, an interface is designed and integrated on one of the chamber walls for temperature measurement by an infrared camera. Preliminary measurements are performed on a phantom consisting essentially of water. Experimental results of the phantom temperature rise are in good agreement with theoretical predictions. This confirms thal the designed reverberation chamber allows to expose the deviee under test with a statistically uniform and calibrated power. Such a deviee is a valuable asse! for EMC testing of electronic equipments in the 26.5 to 60 GHz frequency range. This RC could also permit to conduct preliminary tests in the context of the millimeter waves interactions with being organisms.

Prof. F. Lombard

Statisticians are interested in testing the structure of covariance matrices, especially under the high-dimensional scenario in which the dimensionality of data matrices exceeds the sample size. Many test statistics have been introduced to test whether the covariance matrix is equal to identity structure (<img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?H_%7B01%7D:%20%5CSigma%20=%20I_p" />), sphericity structure (<img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?H_%7B02%7D:%20%5CSigma%20=%20%5Csigma%5E2I_p" />) or diagonal structure (<img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?H_%7B03%7D:%20%5CSigma%20=%20diag(d_1,%20d_2,%5Cdots,d_p)" />). These test statistics work under the assumption that data follows the multivariate normal distribution. In our thesis work, we want to compare the performance of test statistics for each structure test under given assumptions and when the distributional assumption is violated, and compare the test sensitivity to outliers. We apply simulation studies with the help of significance level, power of test, and goodness of fit tests to evaluate the performance of structure test statistics. In conclusion, we identify the recommended test statistics that perform well under different scenarios. Moreover, we find out that the test statistics for the identity structure test are more sensitive to the changes of distribution assumptions and outliers compared with others. The test statistics for the diagonal structure test have a better tolerant to the change of the data matrices.

Digital twins have become a large part of new cyber-physical systems as they allow for the simulation of a physical object in the digital world. In addition to the new approaches of digital twins, machines have become more intelligent, allowing them to produce more data than ever before. Within the area of digital twins, there is a need for a less complex approach than a fully optimised digital twin. This approach is more like a digital shadow of the physical object. Therefore, the focus of this thesis is to study machine states and statistical distributions for all sensors in a machine. Where as majority of studies in the literature focuses on generating data from a digital twin, this study focuses on what characteristics a digital twin have. The solution is by defining a term named digital machine template that contains the states and statistical properties of each sensor in a given machine. The primary approach is to create a proof of work application that uses traditional data mining technologies and clustering to analyze how many states there are in a machine and how the sensor data is structured. It all results in a digital machine template with all of the information mentioned above. The results contain all the states a machine might have and the possible statistical distributions of each senor in each state. The digital machine template opens the possibility of using it as a basis for creating a digital twins. It allows the time of development to be shorter than that of a regular digital twin. More research still needs to be done as the less complex approach may lead to missing information or information not being interpreted correctly. It still shows promises as a less complex way of looking at digital twins since it may become necessary due to digital twins becoming even more complex by the day.

Binomial AR(1) process is a model for integer-valued time series with a fi- nite range and discrete time. It has the binomial marginal distribution and the AR(1)-like autocorrelation structure. This thesis deals with deriving some ba- sic properties of this process, methods of parameter estimation and goodness of fit testing. Three methods of parameter estimation are presented: Yule-Walker, the conditional least squares and the maximum likelihood method together with proofs of their asymptotical properties. Next, the goodness of fit testing is pre- sented. At first, two known methods based on the marginal distribution and the autocorrelation function are summarized. Then our own method is added, based on the probability generating function. Several simulations are provided to show the properties of all tests. The application of this model is illustrated on a real dataset. 1

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