Series Estimation in Partially Linear In-Slide Regression Models

The partially linear in-slide model (PLIM) is a useful tool to make econometric analyses and to normalize microarray data. In this article, by using series approximations and a least squares procedure, we propose a semiparametric least squares estimator (SLSE) for the parametric component and a series estimator for the non-parametric component. Under weaker conditions than those imposed in the literature, we show that the SLSE is asymptotically normal and that the series estimator attains the optimal convergence rate of non-parametric regression. We also investigate the estimating problem of the error variance. In addition, we propose a wild block bootstrap-based test for the form of the non-parametric component. Some simulation studies are conducted to illustrate the finite sample performance of the proposed procedure. An example of application on a set of economical data is also illustrated.