Parametric Estimation And Test For Individual Effects In Varying-coefficient Partially Linear EV Models With Longitudinal Data

Longitudinal data is a kind of common data type in practical analysis, which contains both time series data and cross section data and can provide very useful information on the study of dynamic performance. There are many types of models and methodologies to analysis longitudinal data on statistics, while varying coefficient partially linear model has been widely applied in both statistics and economics domains due to its strong ability of explaining and flexibility. However, some measurement errors commonly exist in the actual measurement data. So a varying-coefficient partially linear EV model with longitudinal data has a strong practical significance, and becomes one of the key subjects in statistical studies.In this paper, we investigate the parametric estimation and test for individual effects in varying-coefficient partially linear EV Models with longitudinal data. Firstly, we conduct estimators for both the parametric and nonparametric components at the random effects and fixed effects respectively by the least square estimation method and the local linear estimation method without considering the measurement errors. Moreover, the modified estimators are obtained based on mean deviation and rectification when considering the covariate with measurement errors, which are proved to be consistent and asymptotically normally distributed. To identify the type of individual effects, the parametric Hausman test statistic is proposed to test them. We respectively propose a parametric Hausman test statistic for testing the null hypothesis of random effects against fixed effects in varying-coefficient partially linear EV model under big sample size and small sample size. We prove that the parametric Hausman test statistic is asymptotic compliance standard chi-square distribution under the hypothesis of random effect model for big sample in theory and the simulation result show that the estimators of the parameters have a good estimation effect and the parametric Hausman test statistic is asymptotic compliance standard chi-square distribution under the hypothesis of random effect model. However, we obtain the rejection region of the tests by combining the Bootstrap sampling method and the parametric Hausman test statistic for small sample. And calculate the testing power function by simulation experiments and the simulation indicates that our proposed test statistic have satisfactory sample performance.