Simulation-Based Finite and Large Sample Tests in Multivariate Regressions

Jean-Marie Dufour () and Lynda Khalaf

Cahiers de recherche from Universite de Montreal, Departement de sciences economiques

Abstract: 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.

Keywords: multivariate linear regression; seemingly unrelated regressions; uniform linear hythesis; Monte Carlo test; bounds test; nonlinear hythesis; finite same test; exact test; bootstrap (search for similar items in EconPapers)
JEL-codes: C15 C20 C42 (search for similar items in EconPapers)
Pages: 24 pages
Date: 2000
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://hdl.handle.net/1866/334 (application/pdf)

Related works:
Journal Article: Simulation based finite and large sample tests in multivariate regressions (2002)
Working Paper: Simulation Based Finite and Large Sample Tests in Multivariate Regressions (2000)
Working Paper: Simulation-Based Finite and Large Sample Tests in Multivariate Regressions (2000)
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Persistent link: https://EconPapers.repec.org/RePEc:mtl:montde:2000-10

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