Simulation Encompassing: Testing Non-nested Hypotheses

This paper considers simulation-based procedures to compute the Wald encompassing and the Cox test statistics for non-nested models. These simulation estimation procedures are applied to both the encompassing contrast and its covariance matrix in the case of a Wald non-nested test statistic, and both the numerator and the denominator in the Cox test statistic. The proposed procedures are illustrated by the example of comparing a linear with a log-linear model. Monte Carlo studies are conducted for both examples and the results indicate that with simulated covariance matrices, the small sample behaviour of both test statistics is close to that of their asymptotic distributions.