Parameter Estimation Of Partially Linear Single-Index EV Model For Longitudinal Data

In this paper,the problem of parameter estimation for partial linear single-index model with longitudinal data is studied in the case of measurement errors for covariates of single index and linear part respectively.Firstly,we use B-spline to approximate the unknown index function.Then using the weighted least-square method to estimate the model.We apply the modified weighted least squares method to correct the deviation.Then the effectiveness of SIMEX(Simulation-Extrapolation)method to deal with the measurement error problem is verified by simulation.Finally,two examples,Boston house price and CD4,are used to further illustrate the effectiveness of the method.