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Nonlinear Hypotheses, Inequality Restrictions, and Non-nested Hypotheses: Exact Simultaneous Tests in Linear Regressions

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  • Dufour, Jean-Marie

Abstract

In the classical linear model, comparison of two arbitrary hypotheses on the regression coefficients is considered. Problems involving nonlinear hypotheses, inequality restrictions, or non-nested hypotheses are included. Exact bounds on the null distribution of likelihood ratio statistics are derived (based on the central Fisher distribution). As a special case, a bounds test similar to the Durbin-Watson test is proposed. Multiple testing problems are studied: the bounds obtained for a single pair of hypotheses are shown to enjoy a simultaneity property that allows combination of any number of tests. This result extends to nonlinear hypotheses a well-known result given by H. Scheffe for linear hypotheses. A method of building bounds-induced tests is suggested. Copyright 1989 by The Econometric Society.

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  • Dufour, Jean-Marie, 1989. "Nonlinear Hypotheses, Inequality Restrictions, and Non-nested Hypotheses: Exact Simultaneous Tests in Linear Regressions," Econometrica, Econometric Society, vol. 57(2), pages 335-355, March.
  • Handle: RePEc:ecm:emetrp:v:57:y:1989:i:2:p:335-55
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