A New Estimation for Single Index Model with Longitudinal Data in the Presence of Measurement Errors

Longitudinal data is an important type of data that is widely used in sociology, economics, biomedicine, epidemiology and other fields. However, in practical problems, people often encounter the situation that the variable dimension is very high and the variable concerned cannot be directly observed, that is, there is a measurement error. In order to solve such problems, this paper studies the estimation of the longitudinal data order index model with measurement error. Based on local linear method and simulation extrapolation (SIMEX) method, this paper constructs a new method for estimating single-index parameters and nonparametric link functions. The effectiveness of the proposed estimation method is verified by Monte Carlo numerical simulation. Compared with the Naive estimation which ignores the measurement error and the estimation which ignores the intra-individual correlation, the estimation constructed in this paper has a smaller mean square error. Finally, we apply the method in this paper to the actual data analysis of the investment demand of listed companies, and the results show that the measurement error has a significant impact on the parameter estimation in practical problems.