In this paper an efficient estimation methodology for the partially linear models with random effects is proposed. For this, we use the generalized least square estimate (GLSE) and the B-splines methods to estimate the unknowns, and employ the penalized least square method to obtain the estimators of the random effects item. Further, we also consider the estimation for the variance components. Compared with the existing methods, our proposed methodology performs well. The asymptotic properties of the estimators are obtained. A simulation study is carried out to assess the performance of our proposed methodology.
The project was supported by the National Natural
Science Foundation of China (Grant Nos. 11471160; 1110 1114), the National
Statistical Science Research Key Program of China (Grant No. 2013LZ45),
the Fundamental Research Funds for the Central Universities (Grant No.
30920130111015), the Jiangsu Provincial Basic Research Program (Natural
Science Foundation) (Grant No. BK20131345) and sponsored by Qing Lan Project.