The Inference On Partial Linear Models In Longitudinal Data

Longitudinal data taken on each of number of subjects over time arise frequently from many biomedical and scientific areas. It is combine time series and independent data, and the data are usually correlated within subject and independent between subjects. Also, it provides the solid foundation for the practical problems. Under the longitudinal data, in this paper, based on the linear mixed effect model, firstly, two methods based on least squares are proposed to estimate regression parameter and variance component in linear mixed-effects model with errors in covariate. In simulation the efficiency of the two methods are compared, and the result suggest the proposed estimation is practicable for finite samples. In addition, also two methods of estimation of fixed effects varying coefficient models in longitudinal data are proposed, the simulation illustrates that, large sample with a bit of observations, the accuracy of profile kernel estimation is better than two-step estimation, and on the other hand, small sample with a large number of observations, two-step estimation methods is more efficient than profile kernel estimation. And then in the semiparametric varying coefficient mixed effects models, we take the score testing for the variance component of random effects. Simulations show that the tests are close to the nominal level under, the null hypothesis,and the larger sample sizes, the greater powers approach to1. Under some mild conditions, the asymptotic distribution of score test statistics is a chi-squared distribution. Finally, we consider bootstrap test methods for variance component in the semiparametric varying coefficient mixed effects models. Simulation studies are carried out to compare the empirical level of significance of every test methods, and the results suggest the proposed bootstrap methods are practicable for finite samples.