单指标纵向数据模型的估计

Estimation of Single-index Longitudinal Data Models

纵向数据是一类重要的相关性数据,广泛出现在诸多科研领域。单指标模型是多元非参数回归中重要的降维方法,在纵向数据下研究单指标模型是统计研究的热点问题。针对纵向数据单指标模型,提出惩罚改进二次推断函数方法来讨论模型的参数和非参数估计问题。该方法利用多项式样条回归方法逼近模型中的未知联系函数,将联系函数的估计转化为回归样条系数的估计,然后构造关于样条回归系数和单指标系数的惩罚改进二次推断函数,最小化惩罚改进二次推断函数便可得到模型的估计。理论结果显示,估计结果具有相合性和渐近正态性,最后得到了较好的数值模拟结果和实例数据分析结果,结果显示该方法适用于半参数纵向模型的参数和非参数估计问题。

Longitudinal data is a kind of important correlated data,which appears in many scientific research fields.Single index model is an important dimension reduction method in multivariate non-parametric regression.Research on single index model based on longitudinal data is a hot issue in statistical research.In this paper,we propose a penalized improved method for single-index models with longitudinal data.We first approximate the unknown link function using regression splines method and construct the penalized improved quadratic inference function of regression parameter of spline and coefficient of single index,then get the estimator by minimizing the objective function.Theoretical results show that the estimator has consistency and asymptotic normality and efficiency.Furthermore,we get good numerical simulation results and real data analysis results,which show that the proposed method is suitable for parameter and non-parameter estimation of semi-parametric longitudinal model.