In this research, the nonparametric technique has been presented to estimate the time-varying coefficients functions for the longitudinal balanced data that characterized by observations obtained through (n) from the independent subjects, each one of them is measured repeatedly by group of specific time points (m). Although the measurements are independent among the different subjects; they are mostly connected within each subject and the applied techniques is the Local Linear kernel LLPK technique. To avoid the problems of dimensionality, and thick computation, the two-steps method has been used to estimate the coefficients functions by using the two former technique. Since, the two-steps method depends, in estimation, on (OLS) method, which is sensitive for the existence of abnormality in data or contamination of error; robust methods have been proposed such as LAD & M to strengthen the two-steps method towards the abnormality and contamination of error. In this research imitating experiments have been performed, with verifying the performance of the traditional and robust methods for Local Linear kernel LLPK technique by using two criteria, for different sample sizes and disparity levels.
