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....