This note seeks to clarify whether applications of Cox's (1961) modified likelihood ratio principle logically require a two- or one-tailed test. Logic requires the test of discrimination be one-tailed and the significance test for non-nested hypotheses be two-tailed. The significance test of a...

This paper attempts to synthesize various procedures for testing non-nested hypotheses within the framework of artificial nesting, and establishes the result that different tests correspond to different treatments of its identification problem. Numerical and a priori identification methods are...

Within the framework of linear regression, errors arising from artificial inclusion or exclusion of variables are considered with augmentations or restrictions on a given maintained hypothesis. This permits exploitation of relations between tests based on Wald and Lagrange Multiplier Principles....

This note applies the traditional analysis of specification error to the Cox-tests for separate regression models. Incorrect inclusion of variables in the alternative model leads to consistent tests of the null, whereas incorrect exclusion of variables from the alternative may render the tests...

The first paper demonstrates that Theil's (1961) minimum error variance criterion is asymptotically valid for choosing between non-nested non-linear regression models, as long as one of the models is 'true'. The second paper shows that when the null and alternative hypotheses are separate...