Accounting for time series errors in partially linear model with single- or multiple-run

This paper concerns statistical estimation of the partially linear model (PLM) for time course measurements, which are temporally correlated and allow multiple-run for repeated measurements to enhance experimental accuracy without extending the number of time points within each trial. Such features arise naturally from biomedical data in for e.g. brain fMRI and call for special treatment beyond classical methods in either a purely nonparametric regression model or a PLM with independent errors. We develop a stepwise procedure for estimating the parametric and nonparametric components of the multiple-run PLM and making inference for parameters of interest, adaptive to either single- or multiple-run, in the presence of error temporal dependence. Simulation study and real fMRI data applications illustrate the computational simplicity and effectiveness of the proposed methods. Supplementary material for this paper is available online.