Profile Likelihood Inferences On The Partially Linear Model With A Diverging Number Of Parameters

In this paper, we introduce a profile least squares technique for estimating the para-metric component and study the statistical inferences on the partially linear model with a diverging number of parameters. The main focus is the examination of whether the profile likelihood technique is still applicable to the testing problem for the parametric component of this model. We construct the profile likelihood ratio statistic which is based on comparing the residual sum of squares under null and alternative hypothesis. The asymptotic distribution of the profile likelihood ratio statistic and the power of test are proposed under some regularity conditions, which provide a simple and useful method for statistical inferences on the partially linear model when the number of parameters grows with the sample size. Numerical studies confirm our theory.