Nonlinear hypotheses, inequality restrictions, and non-nested hypotheses: exact simultaneous tests in linear regressions

In the context of the classical linear model, the problem of comparing two arbitrary hypotheses on the regression coefficients is considered. Problems involving nonlinear hypotheses, inequality restrictions, or non-nested hypotheses are included as special cases. Exact bounds on the null distribution of likelihood ratio statistics are derived. In an important special case, a bounds test similar to the Durbin-Watson test is proposed. Multiple testing problems are also studied