Lafaye de Micheaux P. Test de normalité pour les résidus d'un modèle ARMA. Master's thesis (DEA), Université Montpellier II et École Nationale Supérieure Agronomique de Montpellier, 127 pages, June 1998.
Ducharme G. and Lafaye de Micheaux P. Goodness-of-fit tests of normality for the innovations in ARMA models. Technical report number 02-02, Groupe de biostatistique et d'analyse des systèmes, Université Montpellier II, 34 pages, February 2002.
Lafaye de Micheaux P. Méthodes statistiques multivariées en IRMF. Mémoire de Master 2 Recherche, Institut National Polytechnique de Grenoble, 92 pages, June 2007. (In french).
Coeurjolly J.-F., Drouilhet, R., Lafaye de Micheaux P. et Robineau, J.-F. (February 2009). asympTest: an R package for performing parametric statistical tests and confidence intervals based on the central limit theorem. Technical report hal-00358375. Laboratoire Jean Kuntzmann. Université de Grenoble, 18 pages.
Bordier C., Dojat, M. and Lafaye de Micheaux P. (December 2010). Temporal and Spatial Independent Component Analysis for fMRI data sets embedded in a R package, arXiv 1012.0269v1, 23 pages.
Tabelow K., Clayden J.D., Lafaye de Micheaux P., Polzehl J., Schmid V.J., Whitcher B. (December 2010). Image Analysis and Statistical Inference in Neuroimaging with R, Technical report 1578, Weierstrass Institute for Applied Analysis and Stochastics, 9 pages.
PUBLICATIONS details.
[1]Test de normalité pour les résidus d'un modèle ARMA, June 1998.
Abstract: The results contained in this document cast a new light on the important problem of testing the residuals of an ARMA model. Indeed, the validation stage when fitting a model to data, is the determinant step in selecting the best model. The Box and Jenkin's three stages method ends with the validation step which requires the portmanteau test. An advantage of such portmanteau tests is that they pool information from the correlations at different lags. However, a real disadvantage is that they frequently fail to reject poorly fitting models. In practice, they are more useful in disqualifying unsatisfactory models than for selecting the best-fitting model among closely competing candidates. We need to stress that if it can be assumed that the white noise process of an ARMA process is Gaussian, then stronger conclusions can be drawn from the fitted model. For example, not is it only possible to specify an estimated mean squarred error for predicted values, but asymptotic prediction confidence bounds can also be computed. This being so, we propose to replace the portmanteau test with the one we developp here which is targeted at testing normality.
Localisation 1: Bibliothèque de l'Université Montpellier II. Author : Lafaye de Micheaux, Pierre Title : Test de normalité pour les résidus d'un modèle ARMA / Pierre Lafaye de Micheaux Editor : Montpellier : Université Montpellier II Sciences et Techniques du Languedoc, [1998] Collation : 127 f. ; 30 cm Note : thèse Mém. D.E.A. : Biostatistique-Option Agron.-Santé : Montpellier 2 : 1998 Subject : Biométrie -- thèses Link: Link to bibliographical entry
Localisation 2: Bibliothèque de l'ENSAM. Title : Test de normalité pour les résidus d'un modèle ARMA Author : Lafaye de Micheaux, Pierre Source : Mémoire DEA : Biostatistique : ENSA-M Ecole nationale supérieure agronomique de Montpellier (FRA : 30/06/1998 Pages : 126 p. + ann. Subject : DEA BIOSTATISTIQUE Bibliothèque de l'AGRO BIOM/M 78 Link: Link to bibliographical entry
[2]Goodness-of-fit tests of normality for the innovations in ARMA models, Février 2002.
Technical report number 02-02. Groupe de Biostatistique et d'Analyse des systèmes. Université Montpellier II
Abstract: In this paper, we propose a goodness-of-fit test of normality for the innovations of an ARMA(p,q) model with known mean or trend. The test is based on the data-driven smooth test approach and is simple to perform. An extensive simulation study is conducted to see if, for moderate sample sizes, the test holds its level throughout the parameter space. The power of the procedure is also explored by simulation. It is found that our test is generally more powerful than existing tests while holding its level throughout most of the parameter space and thus, can be recommended. This meshes with theoretical results showing the superiority of the data-driven smooth test approach in related contexts.
[3]Méthodes statistiques multivariées en IRMF, June 2007. (In french).
Abstract: The functional magnetic resonance imaging (fMRI) is a new neuroimaging technique that can localize neuronal activiy with a great spatial precision and with a good temporal precision. To detect activated areas in the brain, this method uses local blood oxygenation variations which are reflected by small variations in a certain kind of images obtained by magnetic resonance. The ability to obtain a functional map of the brain non invasively gives new opportunities to disentangle mysteries of the human brain. In this thesis, we describe some non parametric methods of multivariate analysis of fMRI data: Principal component analysis, Independant component analysis and Projection pursuit. We also try to explain the links between these methods, the different views one can have on them and we deal with underlying spatial and temporal aspects. We also provide a computer tool that can simulate, in a very simplified way, fMRI brain signals. This tool enable one to artificially generate fMRI data for which we control many parameters. It will serve as a basis to compare quantitatively the statistical methods presented. We also apply these various statistical methods on a real data set obtained from a human visual fMRI experiment. At least, we propose various avenues of research that could be explored to pursue this preliminary work.
[4]asympTest: an R package for performing parametric statistical tests and confidence intervals based on the central limit theorem, February 2009.
Abstract: This paper describes an R package implementing large sample tests and confidence intervals (based on the central limit theorem) for various parameters. The one and two sample mean and variance contexts are considered. The statistics for all the tests are expressed in the same form, which facilitates their presentation. In the variance parameter cases, the asymptotic robustness of the classical tests depends on the departure of the data distribution from normality measured in terms of the kurtosis of the distribution.
[5]Temporal and Spatial Independent Component Analysis for fMRI data sets embedded in a R package, December 2010.
Abstract: For statistical analysis of functional Magnetic Resonance Imaging (fMRI) data sets, we propose a data-driven approach based on Independent Component Analysis (ICA) im- plemented in a new version of the AnalyzeFMRI R package. For fMRI data sets, spatial dimension being much greater than temporal dimension, spatial ICA is the tractable ap- proach generally proposed. However, for some neuroscientific applications, temporal inde- pendence of source signals can be assumed and temporal ICA becomes then an attracting exploratory technique. In this work, we use a classical linear algebra result ensuring the tractability of temporal ICA. We report several experiments on synthetic data and real MRI data sets that demonstrate the potential interest of our R package.
[6]Image Analysis and Statistical Inference in Neuroimaging with R, December 2010.
Abstract: R is a language and environment for statistical computing and graphics. It can be considered an alternative implementation of the S language developed in the 1970s and 1980s for data analysis and graphics (Becker and Chambers, 1984; Becker et al., 1988). The R language is part of the GNU project and offers versions that compile and run on almost every major operating system currently available. We highlight several R packages built specifically for the analysis of neuroimaging data in the context of functional MRI, diffusion tensor imaging, and dynamic contrast-enhanced MRI. We review their methodology and give an overview of their capabilities for neuroimaging. In addition we summarize some of the current activities in the area of neuroimaging software development in R.
