Testing Linear and Loglinear Regressions against Box-Cox Alternatives

A new procedure is proposed for testing the null hypothesis that a regression model is linear or loglinear against the alternative of a Box-Cox regression. The test statistic, which is based on a novel form of the Lagrange Multiplier test, may be computed by means of an artificial linear regression. Monte Carlo results confirm that it works well, in contrast to the procedure of Andrews (1971), which lacks power, and the Lagrange Multiplier test proposed by Godfrey and Wickens (1981), which is poorly behaved in small samples. The test also works well in an empirical example. Regression lineaire et log-line'aire: un nouvel usage de laformulation Box-Cox. Les auteurs proposent une nouvelle faqon de mettre a la question l'hypothese nulle qu'un modele de regression est lineaire ou log-lineaire en utilisant le modele Box-Cox. On peut calculer le test statistique, base sur une formulation nouvelle du test employant le multiplicateur de Lagrange, en utilisant une regression lineaire artificielle. On montre que cette procedure fonctionne bien en utilisant les methodes de Monte Carlo. I1 appert que cette procedure est superieure par rapport a celle de Andrews (1971) qui manque de robustesse et par rapport a celle de Godfrey et Wickens (1981) qui a des resultats erratiques quand les echantillons sont petits. Les auteurs montrent que la procedure fonctionne bien avec un exemple empirique.

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