A Two-Stage Approach for Semilinear In-Slide Models.

The semilinear in-slide models (SLIMs) have been shown to be effective method for normalizing microarray data (Fan, et al. 2004). Using a backfitting method, Fan, Peng and Huang (2005) proposed a profile least squares (PLS) estimation for the parametric and nonparametric components. The general asymptotic properties for their estimator is not developed. In this paper, we consider a new approach, two-stage estimation, which enables us to establish the asymptotic normalities for both of the parametric and nonparametric component estimators. We further propose a plug-in bandwidth selector using the asymptotic normality of the nonparametric component estimator. The proposed method allow for the modeling of the aggregated SLIMs case where we can explicitly show that taking the aggregated information into account can improve both of the parametric and nonparametric component estimator by the proposed two-stage approach. Some simulation studies are conducted to illustrate the finite sample performance of the proposed procedures.