Asymptotic Distribution-free Tests for Semiparametric Regressions

This article proposes a new general methodology for constructing nonparametric asymptotic distribution-free tests for semiparametric hypotheses in regression models. Tests are based on the difference between the estimated restricted and unrestricted regression errors’ distributions. A suitable integral transformation of this difference renders the tests asymptotically distribution-free, with limits that are well-known functionals of a standard normal variable. Hence, the tests are straightforward to implement. The general methodology is illustrated with applications to testing for parametric models, semiparametric constrained mean-variance models and nonparametric significance. Several Monte Carlo studies show that the finite sample performance of the proposed tests is satisfactory in moderate sample sizes. ∗Corresponding address: Institute of Statistics, Voie du Roman Pays 20, 1348 Louvain-la-Neuve, Belgium. Email: [email protected].