Sur les tests lisses d'ajustement dans le context des series chronologiques

La plupart des modèles en statistique classique repose sur une hypothèse sur la distribution des données ou sur une distribution sous-jacente aux données. La validité de cette hypothèse permet de faire de l’inférence, de construire des intervalles de confiance ou encore de tester la fiabilité du modèle. La problématique des tests d’ajustement vise à s’assurer de la conformité ou de la cohérence de l’hypothèse avec les données disponibles. Dans la présente thèse, nous proposons des tests d’ajustement à la loi normale dans le cadre des séries chronologiques univariées et vectorielles. Nous nous sommes limités à une classe de séries chronologiques linéaires, à savoir les modèles autorégressifs à moyenne mobile (ARMA ou VARMA dans le cas vectoriel). Dans un premier temps, au cas univarié, nous proposons une généralisation du travail de Ducharme et Lafaye de Micheaux (2004) dans le cas où la moyenne est inconnue et estimée. Nous avons estimé les paramètres par une méthode rarement utilisée dans la littérature et pourtant asymptotiquement efficace. En effet, nous avons rigoureusement montré que l’estimateur proposé par Brockwell et Davis (1991, section 10.8) converge presque sûrement vers la vraie valeur inconnue du paramètre. De plus, nous fournissons une preuve rigoureuse de l’inversibilité de la matrice des variances et des covariances de la statistique de test à partir de certaines propriétés d’algèbre linéaire. Le résultat s’applique aussi au cas où la moyenne est supposée connue et égale à zéro. Enfin, nous proposons une méthode de sélection de la dimension de la famille d’alternatives de type AIC, et nous étudions les propriétés asymptotiques de cette méthode. L’outil proposé ici est basé sur une famille spécifique de polynômes orthogonaux, à savoir les polynômes de Legendre. Dans un second temps, dans le cas vectoriel, nous proposons un test d’ajustement pour les modèles autorégressifs à moyenne mobile avec une paramétrisation structurée. La paramétrisation structurée permet de réduire le nombre élevé de paramètres dans ces modèles ou encore de tenir compte de certaines contraintes particulières. Ce projet inclut le cas standard d’absence de paramétrisation. Le test que nous proposons s’applique à une famille quelconque de fonctions orthogonales. Nous illustrons cela dans le cas particulier des polynômes de Legendre et d’Hermite. Dans le cas particulier des polynômes d’Hermite, nous montrons que le test obtenu est invariant aux transformations affines et qu’il est en fait une généralisation de nombreux tests existants dans la littérature. Ce projet peut être vu comme une généralisation du premier dans trois directions, notamment le passage de l’univarié au multivarié ; le choix d’une famille quelconque de fonctions orthogonales ; et enfin la possibilité de spécifier des relations ou des contraintes dans la formulation VARMA. Nous avons procédé dans chacun des projets à une étude de simulation afin d’évaluer le niveau et la puissance des tests proposés ainsi que de les comparer aux tests existants. De plus des applications aux données réelles sont fournies. Nous avons appliqué les tests à la prévision de la température moyenne annuelle du globe terrestre (univarié), ainsi qu’aux données relatives au marché du travail canadien (bivarié). Ces travaux ont été exposés à plusieurs congrès (voir par exemple Tagne, Duchesne et Lafaye de Micheaux (2013a, 2013b, 2014) pour plus de détails). Un article basé sur le premier projet est également soumis dans une revue avec comité de lecture (Voir Duchesne, Lafaye de Micheaux et Tagne (2016)).

Salivary Gland and Tooth Abnormalities Massively Increase Caries Susceptibility in A Mouse Model of Cleft Lip/Palate

Thesis (Ph.D.)--University of Washington, 2016-04

Statistical Hurdle Models for Single Cell Gene Expression: Differential Expression and Graphical Modeling

Thesis (Ph.D.)--University of Washington, 2016-06

Testing Independence in High Dimensions & Identifiability of Graphical Models

Thesis (Ph.D.)--University of Washington, 2016-06

A genetic two-factor model of the covariation among a subset of Multidimensional Aptitude Battery and Wechsler Adult Intelligence Scale - Revised subtests

The phenotypic and genetic factor structure of performance on five Multidimensional Aptitude Battery (MAB) subtests and one Wechsler Adult Intelligence Scale-Revised (WAIS-R) subtest was explored in 390 adolescent twin pairs (184 monozygotic [MZ]; 206 dizygotic (DZ)). The temporal stability of these measures was derived from a subsample of 49 twin pairs, with test-retest correlations ranging from .67 to .85. A phenotypic factor model, in which performance and verbal factors were correlated, provided a good fit to the data. Genetic modeling was based on the phenotypic factor structure, but also took into account the additive genetic (A), common environmental (C), and unique environmental (E) parameters derived from a fully saturated ACE model. The best fitting model was characterized by a genetic correlated two-factor structure with specific effects, a general common environmental factor, and overlapping unique environmental effects. Results are compared to multivariate genetic models reported in children and adults, with the most notable difference being the growing importance of common genes influencing diverse abilities in adolescence. (C) 2003 Elsevier Inc. All rights reserved.

On a resampling approach for tests on the number of clusters with mixture model-based clustering of tissue samples

We consider the problem of assessing the number of clusters in a limited number of tissue samples containing gene expressions for possibly several thousands of genes. It is proposed to use a normal mixture model-based approach to the clustering of the tissue samples. One advantage of this approach is that the question on the number of clusters in the data can be formulated in terms of a test on the smallest number of components in the mixture model compatible with the data. This test can be carried out on the basis of the likelihood ratio test statistic, using resampling to assess its null distribution. The effectiveness of this approach is demonstrated on simulated data and on some microarray datasets, as considered previously in the bioinformatics literature. (C) 2004 Elsevier Inc. All rights reserved.

The comprehensive osteoarthritis test: a simple index for measurement of treatment effects in clinical trials

Objective. To assess the measurement properties of a simple index of symptom severity in osteoarthritis (OA) of the hips and knees. Methods. Both the Western Ontario and McMaster Universities Osteoarthritis Index (WOMAC) and the proposed new Comprehensive Osteoarthritis Test (COAT) instrument were completed weekly by 125 subjects in the context of a randomized, 12-week, 3 parallel-arm clinical trial. The reliabilities of the various scales were assessed on a weekly basis by use of Cronbach's alpha coefficients. The validity of the COAT total scale was assessed by correlation with the WOMAC total scale on a weekly basis with correlation coefficients, and in terms of the correlations between subject-level intercepts and slopes over time. The relative responsiveness of the WOMAC and COAT total scales was assessed using a multilevel (longitudinal) multivariate (WOMAC, COAT) linear model. Results. The WOMAC and COAT total scales were highly reliable (mean over weeks: WOMAC alpha = 0.98; COAT alpha = 0.97). The correlations between the WOMAC and COAT scales were very high (mean over weeks = 0.92; subject-level intercepts = 0.91, slopes = 0.88). The COAT total scale was significantly more responsive than the WOMAC total scale in the active treatment (34.8% improvement vs 26.8%; p = 0.002). Conclusion. The COAT total scale is simple to administer, reliable, valid, and responsive to treatment effects.

Multivariate genetic analysis of cognitive abilities in an adolescent twin sample

The sources of covariation among cognitive measures of Inspection Time, Choice Reaction Time, Delayed Response Speed and Accuracy, and IQ were examined in a classical twin design that included 245 monozygotic (MZ) and 298 dizygotic (DZ) twin pairs. Results indicated that a factor model comprising additive genetic and unique environmental effects was the most parsimonious. In this model, a general genetic cognitive factor emerged with factor loadings ranging from 0.28 to 0.64. Three other genetic factors explained the remaining genetic covariation between various speed and Delayed Response measures with IQ. However, a large proportion of the genetic variation in verbal (54%) and performance (25%) IQ was unrelated to these lower order cognitive measures. The independent genetic IQ variation may reflect information processes not captured by the elementary cognitive tasks, Inspection Time and Choice Reaction Time, nor our working memory task, Delayed Response. Unique environmental effects were mostly nonoverlapping, and partly represented test measurement error.

Transcriptional profile reveals altered hepatic lipid and cholesterol metabolism in hyposulfatemic NaS1 null mice

Sulfate plays an essential role in human growth and development, and its circulating levels are maintained by the renal Na+-SO42- cotransporter, NaS1. We previously generated a NaS1 knockout ( Nas1(-/-)) mouse, an animal model for hyposulfatemia, that exhibits reduced growth and liver abnormalities including hepatomegaly. In this study, we investigated the hepatic gene expression profile of Nas1(-/-) mice using oligonucleotide microarrays. The mRNA expression levels of 92 genes with known functional roles in metabolism, cell signaling, cell defense, immune response, cell structure, transcription, or protein synthesis were increased ( n = 51) or decreased ( n = 41) in Nas1(-/-) mice when compared with Nas1(-/-) mice. The most upregulated transcript levels in Nas1(-/-) mice were found for the sulfotransferase genes, Sult3a1 ( approximate to 500% increase) and Sult2a2 ( 100% increase), whereas the metallothionein-1 gene, Mt1, was among the most downregulated genes ( 70% decrease). Several genes involved in lipid and cholesterol metabolism, including Scd1, Acly, Gpam, Elov16, Acsl5, Mvd, Insig1, and Apoa4, were found to be upregulated ( >= 30% increase) in Nas1(+/+) mice. In addition, Nas1(+/+) mice exhibited increased levels of hepatic lipid ( approximate to 16% increase), serum cholesterol ( approximate to 20% increase), and low-density lipoprotein ( approximate to 100% increase) and reduced hepatic glycogen ( approximate to 50% decrease) levels. In conclusion, these data suggest an altered lipid and cholesterol metabolism in the hyposulfatemic Nas1(-/-) mouse and provide new insights into the metabolic state of the liver in Nas1(-/-) mice.

Customised birthweight: Coefficients for an Australian population and validation of the model

Background: Published birthweight references in Australia do not fully take into account constitutional factors that influence birthweight and therefore may not provide an accurate reference to identify the infant with abnormal growth. Furthermore, studies in other regions that have derived adjusted (customised) birthweight references have applied untested assumptions in the statistical modelling. Aims: To validate the customised birthweight model and to produce a reference set of coefficients for estimating a customised birthweight that may be useful for maternity care in Australia and for future research. Methods: De-identified data were extracted from the clinical database for all births at the Mater Mother's Hospital, Brisbane, Australia, between January 1997 and June 2005. Births with missing data for the variables under study were excluded. In addition the following were excluded: multiple pregnancies, births less than 37 completed week's gestation, stillbirths, and major congenital abnormalities. Multivariate analysis was undertaken. A double cross-validation procedure was used to validate the model. Results: The study of 42 206 births demonstrated that, for statistical purposes, birthweight is normally distributed. Coefficients for the derivation of customised birthweight in an Australian population were developed and the statistical model is demonstrably robust. Conclusions: This study provides empirical data as to the robustness of the model to determine customised birthweight. Further research is required to define where normal physiology ends and pathology begins, and which segments of the population should be included in the construction of a customised birthweight standard.

Delay estimation for multivariate time series

Most traditional methods for extracting the relationships between two time series are based on cross-correlation. In a non-linear non-stationary environment, these techniques are not sufficient. We show in this paper how to use hidden Markov models (HMMs) to identify the lag (or delay) between different variables for such data. We first present a method using maximum likelihood estimation and propose a simple algorithm which is capable of identifying associations between variables. We also adopt an information-theoretic approach and develop a novel procedure for training HMMs to maximise the mutual information between delayed time series. Both methods are successfully applied to real data. We model the oil drilling process with HMMs and estimate a crucial parameter, namely the lag for return.

Using monthly returns to model conditional heteroscedasticity

This empirical study examines the extent of non-linearity in a multivariate model of monthly financial series. To capture the conditional heteroscedasticity in the series, both the GARCH(1,1) and GARCH(1,1)-in-mean models are employed. The conditional errors are assumed to follow the normal and Student-t distributions. The non-linearity in the residuals of a standard OLS regression are also assessed. It is found that the OLS residuals as well as conditional errors of the GARCH models exhibit strong non-linearity. Under the Student density, the extent of non-linearity in the GARCH conditional errors was generally similar to those of the standard OLS. The GARCH-in-mean regression generated the worse out-of-sample forecasts.

The variant rpoS allele of S. enteritidis strain 27655R does not affect virulence in a chick model nor constitutive curliation but does generate a cold-sensitive phenotype

Adherence of pathogenic Escherichia coli and Salmonella spp. to host cells is in part mediated by curli fimbriae which, along with other virulence determinants, are positively regulated by RpoS. Interested in the role and regulation of curli (SEF17) fimbriae of Salmonella enteritidis in poultry infection, we tested the virulence of naturally occurring S. enteritidis PT4 strains 27655R and 27655S which displayed constitutive and null expression of curli (SEF17) fimbriae, respectively, in a chick invasion assay and analysed their rpoS alleles. Both strains were shown to be equally invasive and as invasive as a wild-type phage type 4 strain and an isogenic derivative defective for the elaboration of curli. We showed that the rpoS allele of 27655S was intact even though this strain was non-curliated and we confirmed that a S. enteritidis rpoS::strr null mutant was unable to express curli, as anticipated. Strain 27655R, constitutively curliated, possessed a frameshift mutation at position 697 of the rpoS coding sequence which resulted in a truncated product and remained curliated even when transduced to rpoS::strr. Additionally, rpoS mutants are known to be cold-sensitive, a phenotype confirmed for strain 27655R. Collectively, these data indicated that curliation was not a significant factor for pathogenesis of S. enteritidis in this model and that curliation of strains 27655R and 27655S was independent of RpoS. Significantly, strain 27655R possessed a defective rpoS allele and remained virulent. Here was evidence that supported the concept that different naturally occurring rpoS alleles may generate varying virulence phenotypic traits.

Emulation of dynamic computer models with multivariate output

This preliminary report describes work carried out as part of work package 1.2 of the MUCM research project. The report is split in two parts: the ?rst part (Sections 1 and 2) summarises the state of the art in emulation of computer models, while the second presents some initial work on the emulation of dynamic models. In the ?rst part, we describe the basics of emulation, introduce the notation and put together the key results for the emulation of models with single and multiple outputs, with or without the use of mean function. In the second part, we present preliminary results on the chaotic Lorenz 63 model. We look at emulation of a single time step, and repeated application of the emulator for sequential predic- tion. After some design considerations, the emulator is compared with the exact simulator on a number of runs to assess its performance. Several general issues related to emulating dynamic models are raised and discussed. Current work on the larger Lorenz 96 model (40 variables) is presented in the context of dimension reduction, with results to be provided in a follow-up report. The notation used in this report are summarised in appendix.

A multivariate examination of the relationship between strategic planning and organisational performance

Strategic planning and more specifically, the impact of strategic planning on organisational performance has been the subject of significant academic interest since the early 1970's. However, despite the significant amount of previous work examining the relationship between strategic planning and organisational performance, a comprehensive literature review identified a number of areas where contributions to the domain of study could be made. In overview, the main areas for further study identified from the literature review were a) a further examination of both the dimensionality and conceptualisation of strategic planning and organisational performance and b) a further, multivariate, examination of the relationship between strategic planning and performance, to capture the newly identified dimensionality. In addition to the previously identified strategic planning and organisational performance constructs, a comprehensive literature based assessment was undertaken and five main areas were identified for further examination, these were a) organisational b) comprehensive strategic choice, c) the quality of strategic options generated, d) political behavior and e) implementation success. From this, a conceptual model incorporating a set of hypotheses to be tested was formulated. In order to test the conceptual model specified and also the stated hypotheses, data gathering was undertaken. The quantitative phase of the research involved a mail survey of senior managers in medium to large UK based organisations, of which a total of 366 fully useable responses were received. Following rigorous individual construct validity and reliability testing, the complete conceptual model was tested using latent variable path analysis. The results for the individual hypotheses and also the complete conceptual model were most encouraging. The findings, theoretical and managerial implications, limitations and directions for future research are discussed.