纵向数据下广义线性模型的稳健二次推断函数估计

Robust quadratic inference functions for generalized linear models with longitudinal data

针对纵向数据下的广义线性模型,为了有效控制离群点对估计的影响以及进一步提高估计的效率,利用二次推断函数(QIF)改进加权的指数得分函数,得到了模型参数有效且稳健的二次推断函数估计(ERQIF),并证明了在一定条件下所得估计的相合性和渐近正态性。数值计算结果进一步表明,当离群点存在或工作相关矩阵被错误指定时,所得估计有稳健的模拟结果。

This paper presents an efficient and robust estimation method for generalized linear models with longitu- dinal data. By using a quadratic inferential function （QIF） to improve the weighted exponential score function, we can obtain an effective and robust quadratic inferential function （ERQIF）. Under some regularity conditions, the resulting estimators are consistent and asymptotically normal distributed. Finally, simulation studies show that the proposed estimators have robust and efficient numerical results, even when many outliers are included and the work- ing correlation matrix is misspecified.