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

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.