Smoothing Estimating Functions In Quantile Partially Linear Varying Coefficient Models With Longitudinal Data

Partially linear varying coefficient model retains the advantages of the linear model that it is easy to explain. And it has the ability to dimension reduction when comparing with the non-parametric model, and is more flexible than simple variable coefficient model, leading to a broader applicability. Currently, partially linear varying coefficient model has been widely applied to biomedicine, econometrics and other related fields.Quantile regression has robustness by using the conditional quantile of dependent and independent variables to construct model. Study of complex data is an important content of statistics in which the longitudinal data is one of the types of complex data. For longitudinal data, the difficulty lies in how to deal with the correlation between the inter-cluster individual.In this paper, the statistical methods of quantile partially linear varying coefficient models and the properties of large sample have been studied under longitudinal data,and the details are as follows:Firstly, a new estimation procedure is proposed for the partial linear variable coefficient model with longitudinal data, based on quantile regression and B spline basis function approximating function coefficients. The proposed method avoids the loss of efficiency by taking into account the intra group correlation among the same sample observations. At the same time, the estimators of parameters and the covariance matrix are obtained by using the induced smoothing method. The empirical results show that the new method is more stable and effective than the conditional mean method for outliers or heavy-tail correlated errors.Secondly, under some regularity condition, it is proved that the asymptotic normality of the parameter estimators and the function coefficient estimators have the optimal convergence rate.Thirdly, use the simulation study and empirical analysis to verify the finite sample performance of the proposed induced smoothing method, while the empirical analysis also shows the practical property of the proposed estimation.