Cross-validated Bandwidths and Significance Testing

The development of an asymptotic theory relating to the size of a bandwidth of a variable that is entered into a nonparametric regression is becoming well understood. However, the connections between variables that are smoothed away and those that are tested for significance has not been previously studied. This paper proposes a variety of simulation exercises to examine the performance of both cross-validated bandwidths and individual and joint tests of significance. We focus on settings where the hypothesis of interest focuses only on continuous variables, only on discrete variables, and finally a mix of discrete and continuous variables and uses tests that can handle either data type individually as well as jointly. Our results suggest that individual tests of significance and variable specific bandwidths are very close in performance, but joint tests and joint bandwidth recognition produce substantially different results. This underscores the importance of testing for joint significance when one is trying to arrive at the final nonparametric model of interest.