*Journal of Econometrics* 21 (1983) 5-33.

**
THE NULL AND NON-NULL ASYMPTOTIC DISTRIBUTION OF THE COX TEST
FOR MULTIVARIATE NONLINEAR REGRESSION ALTERNATIVES
AND A NEW DISTRIBUTION-FREE COX TEXT*
**

**Victor AGUIRRE-TORRES and A. Ronald GALLANT**

North Carolina State University, Raleigh, NC 27650-5457, USA

The asymptotic distribution of the generalized Cox test for choosing between two multivariate nonlinear regression models in implicit form is derived. The data is assumed to be generated by a model that need not be either the null or the non-null model. As the data-generating model is not subjected to a Pitman drift the analysis is global, not local, and provides a fairly complete qualitative description of the power characteristics of the generalized Cox test. Some investigations of these characteristics are included. A new test statistic is introduced that does not require an explicit specification of the error distribution of the null model. The idea is to replace an analytical computation of the expectation of the Cox difference with a bootstrap estimate. The null distribution of this new test is derived.