Comparison of Nonparametric Components in Two Partially Linear Models

In this article, we are concerned with whether the nonparametric functions are parallel from two partial linear models, and propose a test statistic to check the difference of the two functions. The unknown constant α is estimated by using moment method under null models. Nonparametric functions under both null and full models are estimated by using local linear method. The asymptotic properties of parametric and nonparametric components are derived. The test statistic under the null hypothesis is calculated and shown to be asymptotically normal.