指数平方损失下变系数部分非线性模型的估计

ESTIMATION FOR VARYING COEFFICIENT PARTIALLY NONLINEAR MODELS BASED ON EXPONENTIAL SQUARED LOSS FUNCTION

本文对变系数部分非线性模型基于指数平方损失的方法进行稳健估计,这种方法不受异常值和重尾误差的影响,稳定性强.其中对变系数部分使用了B样条基函数进行逼近.在一定的正则条件下,我们建立并证明了估计量的渐近性质.

In this paper, we propose a robust estimation method based on the exponential squared loss function for the varying coefficient partially nonlinear model. This method has strong stability because it is not affected by outliers and heavy tail error distribution. The nonparametric functions are approximated by B-spline basis functions. Under the regularity conditions, the asymptotic properties of proposed estimators are established and proved.