In the last few decades, longitudinal data was deeply research
in statistics science and widely used in many field, such as finance, medical science,
agriculture and so on. The characteristic of longitudinal data is that the values are
independent from different samples but they are correlate from one sample. Many
nonparametric estimation methods were applied into longitudinal data models with development
of computer technology. Using Cholesky decomposition and Profile least squares estimation,
we will propose a effective spline estimation method pointing at nonparametric model of
longitudinal data with covariance matrix unknown in this paper. Finally, we point that
the new proposed method is more superior than Naive spline estimation in the covariance
matrix is unknown case by comparing the simulated results of one example.