Estimating And Testing In Semi-Parametric Varying Coefficient Model With Longitudinal Data

Longitudinal data is one of the analysis data commonly used in statistical. Relative to the cross-sectional data, longitudinal data not only is a repeatable measurement data type, but also avoid the disorder versus sectional data. Because of its strong adaptability and widely practical applications in recent years, and the model provide important solutions to solve practical problems in economics, biomedical.and other financial areas. Regression analysis is one of the most commonly methods used in varying coefficient models. Varying coefficient model is one of semi-parametric models widely studied. And semi-parametric varying coefficient model is one of the models that used widely in longitudinal data.In this paper, we propose profile-likelihood estimators for both the parametric and nonparametric components in the semi-parametric varying coefficient models with fixed effects and random effects, and establish asymptotic normality for all of the estimators. In addition, we present another method called nonparametric method to estimate the varying coefficient. Compared with the previous estimate methods, this method shortens the estimated time. More importantly, we introduce a method for testing the null hypothesis of random effects against fixed effects in semi-parametric varying coefficient models with longitudinal data. For the parametric part, we use Hausman test as an alternative to the fixed effects or random effects estimators for longitudinal data. And for varying coefficient, we propose nonparametric Hausman test statistic for testing random effects or fixed effects. Monte Carlo simulations show that our proposed testing methods have satisfactory finite sample performance.