This paper examines the consistency properties of some tests of a null model against a single non-nested alternative and against multiple non-nested alternatives (paired and joint tests, respectively). Consistency of the tests is evaluated. First, even when all possible paired comparisons are...

This paper is concerned with the problem of testing one form of covariance structure against another in a normal linear regression. All point-optimal tests recently proposed by King and his associates can be interpreted as special cases of the Cox test for non-nested hypotheses. This provides a...

It is argued that the general formulation of point-optimal tests, as summarized in King (1988): i) makes use of a benchmark which is excessively stringent; ii) fails to integrate the method with traditional testing methods; iii) uses data to form a specific null hypothesis; iv) offers no...

Chin and Kennedy (1987) have recently suggested a procedure that they claim can be used to infer the direction of the true model relative to two rejected nonnested hypotheses. This note argues that their procedure can be viewed as model discrimination after model testing has rejected two...

Under appropriate conditions, some asymptotic test statistics based on generalized inverses (g-inverses) are shown to be arbitrary in the sense that any desired numerical value for a statistic can be obtained by appropriately choosing a g-inverse of an estimator. Examples of statistics based on...