基于纵向数部分线性模型的分位数模型平均

Quantile Model Averaging Based on Longitudinal Partial Linear Model

摘要: 本文针对纵向数据部分线性回归模型中的参数估计与非参数估计问题，基于分位数回归估计方法提出了一种稳健的模型平均估计量。为了提高估计效率，采用工作相关矩阵分解和估计方程平滑法处理纵向数据的组内相关性，并通过局部线性估计方法处理模型的非参数部分，给出了模型参数与非参数估计的Newton-Raphson迭代算法。数值模拟表明，新的估计方法具有良好的估计性能。将新估计方法应用到空气质量数据的预测分析中，证明了该方法在实际应用中也具有可行性。

Abstract: Based on the problem of parameter estimation and non-parametric estimation in the partial linear regression model of longitudinal data, this paper proposes a robust model average estimator based on the quantile regression estimation method. In order to improve the estimation efficiency, the working correlation matrix decomposition and estimation equation smoothing method are used to deal with the intra-group correlation of longitudinal data, and the non-parametric part of the model is processed by the local linear estimation method. The Newton-Raphson iterative algorithm for model parameter and non-parametric estimation is given. Numerical simulation shows that the new estimation method has good estimation performance. The new estimation method is applied to the prediction and analysis of air quality data, which proves that the method is also feasible in practical applications.