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.

L’hypoalbuminémie dans les premières 24 heures de l’admission est associée avec la dysfonction d’organes chez les patients brûlés

L’hypoalbuminémie est une trouvaille fréquente chez le patient brulé mais sa relation avec la morbidité et mortalité n’a pas été bien établie. Objectif : Déterminer si l’hypoalbuminémie dans les premières 24 heures suivant l’admission est associée avec la dysfonction d’organes (mesurée avec le score SOFA) chez les patients présentant des brûlures graves. Méthodologie : Nous avons révisé les dossiers médicaux des patients adultes avec de brûlures de 20% ou plus de surface corporelle admis pendant les premières 24 heures à l’unité de grands brulés du CHUM entre les années 2008 et 2009. Nous avons utilisé un modèle de régression linéaire multivariée pour déterminer si l’hypoalbuminémie était un prédicteur indépendant de la dysfonction d’organes. Résultats : 56 sujets ont été analysés. L’analyse de régression linéaire multiple a montré qu’en contrôlant pour l’âge, le sexe, la surface corporelle brûlée et les brûlures par inhalation, l’hypoalbuminémie pendant les premières 24 heures suivant l’admission est un prédicteur indépendant de la dysfonction d’organes. Une concentration d’albumine ≤30g/L est aussi associée à une augmentation de la dysfonction d’organes [score SOFA au jour 0 (p = 0.005), jour 1 (p = 0.005), moyenne de la première semaine (p = 0.004)], mais n’est pas associée avec la mortalité (p = 0.061). Conclusions : L’hypoalbuminémie est associée avec la dysfonction d’organes chez les patients brulés. À la différence de facteurs non modifiables comme l’âge, le sexe, la surface corporelle brûlée et la présence de brûlures par inhalation, la correction de l’hypoalbuminémie peut être un objectif intéressant pour un futur essai clinique.

Simulation-Based Finite and Large Sample Tests in Multivariate Regressions.

In the context of multivariate linear regression (MLR) models, it is well known that commonly employed asymptotic test criteria are seriously biased towards overrejection. In this paper, we propose a general method for constructing exact tests of possibly nonlinear hypotheses on the coefficients of MLR systems. For the case of uniform linear hypotheses, we present exact distributional invariance results concerning several standard test criteria. These include Wilks' likelihood ratio (LR) criterion as well as trace and maximum root criteria. The normality assumption is not necessary for most of the results to hold. Implications for inference are two-fold. First, invariance to nuisance parameters entails that the technique of Monte Carlo tests can be applied on all these statistics to obtain exact tests of uniform linear hypotheses. Second, the invariance property of the latter statistic is exploited to derive general nuisance-parameter-free bounds on the distribution of the LR statistic for arbitrary hypotheses. Even though it may be difficult to compute these bounds analytically, they can easily be simulated, hence yielding exact bounds Monte Carlo tests. Illustrative simulation experiments show that the bounds are sufficiently tight to provide conclusive results with a high probability. Our findings illustrate the value of the bounds as a tool to be used in conjunction with more traditional simulation-based test methods (e.g., the parametric bootstrap) which may be applied when the bounds are not conclusive.

Exact Tests for Contemporaneous Correlation of Disturbances in Seemingly Unrelated Regressions.

This paper proposes finite-sample procedures for testing the SURE specification in multi-equation regression models, i.e. whether the disturbances in different equations are contemporaneously uncorrelated or not. We apply the technique of Monte Carlo (MC) tests [Dwass (1957), Barnard (1963)] to obtain exact tests based on standard LR and LM zero correlation tests. We also suggest a MC quasi-LR (QLR) test based on feasible generalized least squares (FGLS). We show that the latter statistics are pivotal under the null, which provides the justification for applying MC tests. Furthermore, we extend the exact independence test proposed by Harvey and Phillips (1982) to the multi-equation framework. Specifically, we introduce several induced tests based on a set of simultaneous Harvey/Phillips-type tests and suggest a simulation-based solution to the associated combination problem. The properties of the proposed tests are studied in a Monte Carlo experiment which shows that standard asymptotic tests exhibit important size distortions, while MC tests achieve complete size control and display good power. Moreover, MC-QLR tests performed best in terms of power, a result of interest from the point of view of simulation-based tests. The power of the MC induced tests improves appreciably in comparison to standard Bonferroni tests and, in certain cases, outperforms the likelihood-based MC tests. The tests are applied to data used by Fischer (1993) to analyze the macroeconomic determinants of growth.

Markovian Processes, Two-Sided Autoregressions and Finite-Sample Inference for Stationary and Nonstationary Autoregressive Processes.

In this paper, we develop finite-sample inference procedures for stationary and nonstationary autoregressive (AR) models. The method is based on special properties of Markov processes and a split-sample technique. The results on Markovian processes (intercalary independence and truncation) only require the existence of conditional densities. They are proved for possibly nonstationary and/or non-Gaussian multivariate Markov processes. In the context of a linear regression model with AR(1) errors, we show how these results can be used to simplify the distributional properties of the model by conditioning a subset of the data on the remaining observations. This transformation leads to a new model which has the form of a two-sided autoregression to which standard classical linear regression inference techniques can be applied. We show how to derive tests and confidence sets for the mean and/or autoregressive parameters of the model. We also develop a test on the order of an autoregression. We show that a combination of subsample-based inferences can improve the performance of the procedure. An application to U.S. domestic investment data illustrates the method.

Simulation-Based Finite-Sample Tests for Heteroskedasticity and ARCH Effects.

A wide range of tests for heteroskedasticity have been proposed in the econometric and statistics literature. Although a few exact homoskedasticity tests are available, the commonly employed procedures are quite generally based on asymptotic approximations which may not provide good size control in finite samples. There has been a number of recent studies that seek to improve the reliability of common heteroskedasticity tests using Edgeworth, Bartlett, jackknife and bootstrap methods. Yet the latter remain approximate. In this paper, we describe a solution to the problem of controlling the size of homoskedasticity tests in linear regression contexts. We study procedures based on the standard test statistics [e.g., the Goldfeld-Quandt, Glejser, Bartlett, Cochran, Hartley, Breusch-Pagan-Godfrey, White and Szroeter criteria] as well as tests for autoregressive conditional heteroskedasticity (ARCH-type models). We also suggest several extensions of the existing procedures (sup-type of combined test statistics) to allow for unknown breakpoints in the error variance. We exploit the technique of Monte Carlo tests to obtain provably exact p-values, for both the standard and the new tests suggested. We show that the MC test procedure conveniently solves the intractable null distribution problem, in particular those raised by the sup-type and combined test statistics as well as (when relevant) unidentified nuisance parameter problems under the null hypothesis. The method proposed works in exactly the same way with both Gaussian and non-Gaussian disturbance distributions [such as heavy-tailed or stable distributions]. The performance of the procedures is examined by simulation. The Monte Carlo experiments conducted focus on : (1) ARCH, GARCH, and ARCH-in-mean alternatives; (2) the case where the variance increases monotonically with : (i) one exogenous variable, and (ii) the mean of the dependent variable; (3) grouped heteroskedasticity; (4) breaks in variance at unknown points. We find that the proposed tests achieve perfect size control and have good power.

Testing Mean-Variance Efficiency in CAPM with Possibly Non-Gaussian Errors : An Exact Simulation-Based Approach

In this paper we propose exact likelihood-based mean-variance efficiency tests of the market portfolio in the context of Capital Asset Pricing Model (CAPM), allowing for a wide class of error distributions which include normality as a special case. These tests are developed in the frame-work of multivariate linear regressions (MLR). It is well known however that despite their simple statistical structure, standard asymptotically justified MLR-based tests are unreliable. In financial econometrics, exact tests have been proposed for a few specific hypotheses [Jobson and Korkie (Journal of Financial Economics, 1982), MacKinlay (Journal of Financial Economics, 1987), Gib-bons, Ross and Shanken (Econometrica, 1989), Zhou (Journal of Finance 1993)], most of which depend on normality. For the gaussian model, our tests correspond to Gibbons, Ross and Shanken’s mean-variance efficiency tests. In non-gaussian contexts, we reconsider mean-variance efficiency tests allowing for multivariate Student-t and gaussian mixture errors. Our framework allows to cast more evidence on whether the normality assumption is too restrictive when testing the CAPM. We also propose exact multivariate diagnostic checks (including tests for multivariate GARCH and mul-tivariate generalization of the well known variance ratio tests) and goodness of fit tests as well as a set estimate for the intervening nuisance parameters. Our results [over five-year subperiods] show the following: (i) multivariate normality is rejected in most subperiods, (ii) residual checks reveal no significant departures from the multivariate i.i.d. assumption, and (iii) mean-variance efficiency tests of the market portfolio is not rejected as frequently once it is allowed for the possibility of non-normal errors.

Exact Skewness-Kurtosis Tests for Multivariate Normality and Goodness-of-fit in Multivariate Regressions with Application to Asset Pricing Models

We study the problem of testing the error distribution in a multivariate linear regression (MLR) model. The tests are functions of appropriately standardized multivariate least squares residuals whose distribution is invariant to the unknown cross-equation error covariance matrix. Empirical multivariate skewness and kurtosis criteria are then compared to simulation-based estimate of their expected value under the hypothesized distribution. Special cases considered include testing multivariate normal, Student t; normal mixtures and stable error models. In the Gaussian case, finite-sample versions of the standard multivariate skewness and kurtosis tests are derived. To do this, we exploit simple, double and multi-stage Monte Carlo test methods. For non-Gaussian distribution families involving nuisance parameters, confidence sets are derived for the the nuisance parameters and the error distribution. The procedures considered are evaluated in a small simulation experi-ment. Finally, the tests 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.

Méthodes d’inférence exactes pour un modèle de régression avec erreurs AR(2) gaussiennes

Ce texte propose des méthodes d’inférence exactes (tests et régions de confiance) sur des modèles de régression linéaires avec erreurs autocorrélées suivant un processus autorégressif d’ordre deux [AR(2)], qui peut être non stationnaire. L’approche proposée est une généralisation de celle décrite dans Dufour (1990) pour un modèle de régression avec erreurs AR(1) et comporte trois étapes. Premièrement, on construit une région de confiance exacte pour le vecteur des coefficients du processus autorégressif (φ). Cette région est obtenue par inversion de tests d’indépendance des erreurs sur une forme transformée du modèle contre des alternatives de dépendance aux délais un et deux. Deuxièmement, en exploitant la dualité entre tests et régions de confiance (inversion de tests), on détermine une région de confiance conjointe pour le vecteur φ et un vecteur d’intérêt M de combinaisons linéaires des coefficients de régression du modèle. Troisièmement, par une méthode de projection, on obtient des intervalles de confiance «marginaux» ainsi que des tests à bornes exacts pour les composantes de M. Ces méthodes sont appliquées à des modèles du stock de monnaie (M2) et du niveau des prix (indice implicite du PNB) américains

Short run and long run causality in time series: Inference

We propose methods for testing hypotheses of non-causality at various horizons, as defined in Dufour and Renault (1998, Econometrica). We study in detail the case of VAR models and we propose linear methods based on running vector autoregressions at different horizons. While the hypotheses considered are nonlinear, the proposed methods only require linear regression techniques as well as standard Gaussian asymptotic distributional theory. Bootstrap procedures are also considered. For the case of integrated processes, we propose extended regression methods that avoid nonstandard asymptotics. The methods are applied to a VAR model of the U.S. economy.

Exact Multivariate Tests of Asset Pricing Models with Stable Asymmetric Distributions

In this paper, we propose exact inference procedures for asset pricing models that can be formulated in the framework of a multivariate linear regression (CAPM), allowing for stable error distributions. The normality assumption on the distribution of stock returns is usually rejected in empirical studies, due to excess kurtosis and asymmetry. To model such data, we propose a comprehensive statistical approach which allows for alternative - possibly asymmetric - heavy tailed distributions without the use of large-sample approximations. The methods suggested are based on Monte Carlo test techniques. Goodness-of-fit tests are formally incorporated to ensure that the error distributions considered are empirically sustainable, from which exact confidence sets for the unknown tail area and asymmetry parameters of the stable error distribution are derived. Tests for the efficiency of the market portfolio (zero intercepts) which explicitly allow for the presence of (unknown) nuisance parameter in the stable error distribution are derived. The methods proposed are applied to monthly returns on 12 portfolios of the New York Stock Exchange over the period 1926-1995 (5 year subperiods). We find that stable possibly skewed distributions provide statistically significant improvement in goodness-of-fit and lead to fewer rejections of the efficiency hypothesis.

Impact du climat organisationnel sur le façonnement des pratiques relationnelles de soin et la satisfaction professionnelle d’infirmières soignantes en milieu hospitalier

Les pratiques relationnelles de soin (PRS) sont au cœur même des normes et valeurs professionnelles qui définissent la qualité de l’exercice infirmier, mais elles sont souvent compromises par un milieu de travail défavorable. La difficulté pour les infirmières à actualiser ces PRS qui s’inscrivent dans les interactions infirmière-patient par un ensemble de comportements de caring, constitue une menace à la qualité des soins, tout en créant d’importantes frustrations pour les infirmières. En mettant l’accent sur l’aspect relationnel du processus infirmier, cette recherche, abordée sous l'angle du caring, renvoie à une vision novatrice de la qualité des soins et de l'organisation des services en visant à expliquer l’impact du climat organisationnel sur le façonnement des PRS et la satisfaction professionnelle d’infirmières soignantes en milieu hospitalier. Cette étude prend appui sur une adaptation du Quality-Caring Model© de Duffy et Hoskins (2003) qui combine le modèle d’évaluation de la qualité de Donabedian (1980, 1992) et la théorie du Human Caring de Watson (1979, 1988). Un devis mixte de type explicatif séquentiel, combinant une méthode quantitative de type corrélationnel prédictif et une méthode qualitative de type étude de cas unique avec niveaux d’analyse imbriqués, a été privilégié. Pour la section quantitative auprès d’infirmières soignantes (n = 292), différentes échelles de mesure validées, de type Likert ont permis de mesurer les variables suivantes : le climat organisationnel (global et cinq dimensions composites) ; les PRS privilégiées ; les PRS actuelles ; l’écart entre les PRS privilégiées et actuelles ; la satisfaction professionnelle. Des analyses de régression linéaire hiérarchique ont permis de répondre aux six hypothèses du volet quantitatif. Pour le volet qualitatif, les données issues des sources documentaires, des commentaires recueillis dans les questionnaires et des entrevues effectuées auprès de différents acteurs (n = 15) ont été traités de manière systématique, par analyse de contenu, afin d’expliquer les liens entre les notions d’intérêts. L’intégration des inférences quantitatives et qualitatives s’est faite selon une approche de complémentarité. Nous retenons du volet quantitatif qu’une fois les variables de contrôle prises en compte, seule une dimension composite du climat organisationnel, soit les caractéristiques de la tâche, expliquent 5 % de la variance des PRS privilégiées. Le climat organisationnel global et ses dimensions composites relatives aux caractéristiques du rôle, de l’organisation, du supérieur et de l’équipe sont de puissants facteurs explicatifs des PRS actuelles (5 % à 11 % de la variance), de l’écart entre les PRS privilégiées et actuelles (4 % à 9 %) ainsi que de la satisfaction professionnelle (13 % à 30 %) des infirmières soignantes. De plus, il a été démontré, qu’au-delà de l’important impact du climat organisationnel global et des variables de contrôle, la fréquence des PRS contribue à augmenter la satisfaction professionnelle des infirmières (ß = 0,31 ; p < 0,001), alors que l’écart entre les PRS privilégiées et actuelles contribue à la diminuer (ß = - 0,30 ; p < 0,001) dans des proportions fort similaires (respectivement 7 % et 8 %). Le volet qualitatif a permis de mettre en relief quatre ordres de facteurs qui expliquent comment le climat organisationnel façonne les PRS et la satisfaction professionnelle des infirmières. Ces facteurs sont: 1) l’intensité de la charge de travail; 2) l’approche d’équipe et la perception du rôle infirmier ; 3) la perception du supérieur et de l’organisation; 4) certaines caractéristiques propres aux patients/familles et à l’infirmière. L’analyse de ces facteurs a révélé d’intéressantes interactions dynamiques entre quatre des cinq dimensions composites du climat, suggérant ainsi qu’il soit possible d’influencer une dimension en agissant sur une autre. L’intégration des inférences quantitatives et qualitatives rend compte de l’impact prépondérant des caractéristiques du rôle sur la réalisation des PRS et la satisfaction professionnelle des infirmières, tout en suggérant d’adopter une approche systémique qui mise sur de multiples facteurs dans la mise en oeuvre d’interventions visant l’amélioration des environnements de travail infirmier en milieu hospitalier.