7 resultados para multivariate methods

em Université de Montréal, Canada


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Les données du recensement de 2006 de Statistique Canada ont été utilisées afin d’étudier les immigrants diplômés ou certifiés au collégial ou à l’universitaire, tout en essayant de les comparer aux natifs du Québec et du reste du Canada. En fait, nous avons expliqué le fait de détenir un titre postsecondaire du système éducatif québécois chez l’ensemble de la population et chez les différentes générations d’immigrants selon les régions de naissance ou d’origine des individus. De plus, nous avons examiné l’effet de l’âge à l’immigration, de la langue d’usage à la maison et de la période d’arrivée sur le fait de détenir un diplôme ou un certificat postsecondaire du système éducatif québécois. Pour réaliser cette étude, nous avons donc utilisé une analyse bivariée et multivariée axée sur des variables socio-économiques, démographiques, ethnoculturelles et contextuelles. Nous avons trouvé que les natifs du Québec ont des chances supérieures aux autres groupes étudiés (immigrants des diverses régions et natifs du reste du Canada) d’avoir un titre collégial. Cependant, les immigrants, surtout ceux de l’Afrique et de l’Asie de l’Est ou du Sud-est, et les natifs du reste du Canada ont des chances nettement supérieures de détenir un titre universitaire que les natifs du Québec. Les immigrants nés aux États-Unis et en Afrique sont plus souvent diplômés de l’université que ceux nés en Asie de l’Est et du Sud-est. Les Latino-américains de première génération sont plus susceptibles d’avoir un diplôme ou un certificat collégial que les Asiatiques de l’Est ou du Sud-est. Les immigrants de deuxième génération dont la mère est née dans les Caraïbes ou au Québec ont plus de chance de détenir un diplôme ou certificat du collège que les immigrants de deuxième génération dont la mère est née en Asie de l’Est ou du Sud-est. Les enfants qui migrent au Québec ou au Canada avant 10 ans ont des chances nettement plus élevées d’avoir un titre collégial que de ne pas en avoir, en comparaison à ceux arrivés après cet âge. Un immigrant dont la langue d’usage à la maison n’est ni le français ni l’anglais réussit bien au collégial, mais détient moins souvent un titre universitaire. Enfin, la cohorte d’immigrants arrivée durant la période 2000-2006 a significativement plus de chances de détenir un titre universitaire que les autres cohortes étudiées.

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In the context of multivariate regression (MLR) and seemingly unrelated regressions (SURE) models, it is well known that commonly employed asymptotic test criteria are seriously biased towards overrejection. in this paper, we propose finite-and large-sample likelihood-based test procedures for possibly non-linear hypotheses on the coefficients of MLR and SURE systems.

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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.

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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.

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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.

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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.