Testing the Semiparametric Box-Cox Model with Bootstrap

This paper considers tests of the transformation parameter of the Box-Cox model when the distribution of the error is unknown. Monte Carlo experiments are carried out to investigate the rejection probabilities of the GMM-based Wald and Lagrange Multiplier (LM) tests when the null hypothesis is true. The results show that the differences between empirical and nominal levels can be large when asymptotic critical values are used. In most cases, the bootstrap reduces the differences between the empirical and nominal levels, and, in many cases, essentially removes the distortions in levels that occur with asymptotic critical values. Experiments are also carried out to investigate the ability of the bootstrap to provide improved finite-sample critical values with Wald tests based on the semiparametric estimation procedure recently developed by Foster, Tian and Wei (2001).