Probe-level linear model fitting and mixture modeling results in high accuracy detection of differential gene expression

Affiliation: Institut de recherche en immunologie et en cancérologie, Université de Montréal

The Seemingly Unrelated Dynamic Cointegration Regression Model and Testing for Purching Power Parity.

This paper studies seemingly unrelated linear models with integrated regressors and stationary errors. By adding leads and lags of the first differences of the regressors and estimating this augmented dynamic regression model by feasible generalized least squares using the long-run covariance matrix, we obtain an efficient estimator of the cointegrating vector that has a limiting mixed normal distribution. Simulation results suggest that this new estimator compares favorably with others already proposed in the literature. We apply these new estimators to the testing of purchasing power parity (PPP) among the G-7 countries. The test based on the efficient estimates rejects the PPP hypothesis for most countries.

Simulation-Based Finite-Sample Normality Tests in Linear Regressions

In the literature on tests of normality, much concern has been expressed over the problems associated with residual-based procedures. Indeed, the specialized tables of critical points which are needed to perform the tests have been derived for the location-scale model; hence reliance on available significance points in the context of regression models may cause size distortions. We propose a general solution to the problem of controlling the size normality tests for the disturbances of standard linear regression, which is based on using the technique of Monte Carlo tests.

Finite-Sample Diagnostics for Multivariate Regressions with Applications to Linear Asset Pricing Models

In this paper, we propose several finite-sample specification tests for multivariate linear regressions (MLR) with applications to asset pricing models. We focus on departures from the assumption of i.i.d. errors assumption, at univariate and multivariate levels, with Gaussian and non-Gaussian (including Student t) errors. The univariate tests studied extend existing exact procedures by allowing for unspecified parameters in the error distributions (e.g., the degrees of freedom in the case of the Student t distribution). The multivariate tests are based on properly standardized multivariate residuals to ensure invariance to MLR coefficients and error covariances. We consider tests for serial correlation, tests for multivariate GARCH and sign-type tests against general dependencies and asymmetries. The procedures proposed provide exact versions of those applied in Shanken (1990) which consist in combining univariate specification tests. Specifically, we combine tests across equations using the MC test procedure to avoid Bonferroni-type bounds. Since non-Gaussian based tests are not pivotal, we apply the “maximized MC” (MMC) test method [Dufour (2002)], where the MC p-value for the tested hypothesis (which depends on nuisance parameters) is maximized (with respect to these nuisance parameters) to control the test’s significance level. The tests proposed are applied to an asset pricing model with observable risk-free rates, using monthly returns on New York Stock Exchange (NYSE) portfolios over five-year subperiods from 1926-1995. Our empirical results reveal the following. Whereas univariate exact tests indicate significant serial correlation, asymmetries and GARCH in some equations, such effects are much less prevalent once error cross-equation covariances are accounted for. In addition, significant departures from the i.i.d. hypothesis are less evident once we allow for non-Gaussian errors.

Projection-Based Statistical Inference in Linear Structural Models with Possibly Weak Instruments

It is well known that standard asymptotic theory is not valid or is extremely unreliable in models with identification problems or weak instruments [Dufour (1997, Econometrica), Staiger and Stock (1997, Econometrica), Wang and Zivot (1998, Econometrica), Stock and Wright (2000, Econometrica), Dufour and Jasiak (2001, International Economic Review)]. One possible way out consists here in using a variant of the Anderson-Rubin (1949, Ann. Math. Stat.) procedure. The latter, however, allows one to build exact tests and confidence sets only for the full vector of the coefficients of the endogenous explanatory variables in a structural equation, which in general does not allow for individual coefficients. This problem may in principle be overcome by using projection techniques [Dufour (1997, Econometrica), Dufour and Jasiak (2001, International Economic Review)]. AR-types are emphasized because they are robust to both weak instruments and instrument exclusion. However, these techniques can be implemented only by using costly numerical techniques. In this paper, we provide a complete analytic solution to the problem of building projection-based confidence sets from Anderson-Rubin-type confidence sets. The latter involves the geometric properties of “quadrics” and can be viewed as an extension of usual confidence intervals and ellipsoids. Only least squares techniques are required for building the confidence intervals. We also study by simulation how “conservative” projection-based confidence sets are. Finally, we illustrate the methods proposed by applying them to three different examples: the relationship between trade and growth in a cross-section of countries, returns to education, and a study of production functions in the U.S. economy.

Urban Detection From Hyperspectral Images Using Dimension-Reduction Model and Fusion of Multiple Segmentations Based on Stuctural and Textural Features

Ce mémoire de maîtrise présente une nouvelle approche non supervisée pour détecter et segmenter les régions urbaines dans les images hyperspectrales. La méthode proposée n ́ecessite trois étapes. Tout d’abord, afin de réduire le coût calculatoire de notre algorithme, une image couleur du contenu spectral est estimée. A cette fin, une étape de réduction de dimensionalité non-linéaire, basée sur deux critères complémentaires mais contradictoires de bonne visualisation; à savoir la précision et le contraste, est réalisée pour l’affichage couleur de chaque image hyperspectrale. Ensuite, pour discriminer les régions urbaines des régions non urbaines, la seconde étape consiste à extraire quelques caractéristiques discriminantes (et complémentaires) sur cette image hyperspectrale couleur. A cette fin, nous avons extrait une série de paramètres discriminants pour décrire les caractéristiques d’une zone urbaine, principalement composée d’objets manufacturés de formes simples g ́eométriques et régulières. Nous avons utilisé des caractéristiques texturales basées sur les niveaux de gris, la magnitude du gradient ou des paramètres issus de la matrice de co-occurrence combinés avec des caractéristiques structurelles basées sur l’orientation locale du gradient de l’image et la détection locale de segments de droites. Afin de réduire encore la complexité de calcul de notre approche et éviter le problème de la ”malédiction de la dimensionnalité” quand on décide de regrouper des données de dimensions élevées, nous avons décidé de classifier individuellement, dans la dernière étape, chaque caractéristique texturale ou structurelle avec une simple procédure de K-moyennes et ensuite de combiner ces segmentations grossières, obtenues à faible coût, avec un modèle efficace de fusion de cartes de segmentations. Les expérimentations données dans ce rapport montrent que cette stratégie est efficace visuellement et se compare favorablement aux autres méthodes de détection et segmentation de zones urbaines à partir d’images hyperspectrales.