考虑纵向数据下部分线性模型的有效稳健估计问题. 通过结合矩阵的QR 分解技术和二次推断函数方法, 提出了一种基于模态回归的估计过程. 证明了参数分量的估计是相合的, 并给出了其渐近分布. 另外还证明了非参数分量的估计是相合的, 并达到了最优的非参数收敛速度. 数据模拟和实际数据分析结果表明所提出的估计方法具有较好的稳健性和有效性.

This paper considers the efficient and robust estimation for partially linear models with longitudinal data. By combining QR decomposition technique with quadratic inference functions technology, a modal regression based estimation procedure is proposed. We show that the resulting estimator of parametric component is consistent, and obtain the asymptotic normality. In addition, we also show that the resulting estimator of nonparametric component is consistent with the optimal nonparametric convergence rate. Simulation study and real data analysis results indicate the proposed method is more robust and effective.