Abstract: We proposed the test statistic to check whether the nonparametric function in partially linear models is a const or not. We estimated the nonparametric function by the local polynomial method, where we ignored the parametric component, and estimated the parameters by the two stage method. The test statistic under the null hypothesis was calculated, and it was shown to be a symptotically normal.

Key words: partially linear model, local polynomial estimation, two stage estimation, generalized likelihood ratio test