基于指数平方损失的纵向多折点回归模型的稳健估计与统计推断

Robust Estimation and Statistical Inference for Longitudinal Multi-Kink Regression Model Based on Exponential Square Loss

本文基于指数平方损失函数研究纵向多折点回归模型的稳健估计与统计推断问题.为提高参数估计方法的效率,基于局部线性平滑方法和修正的Cholesky分解方法提出纵向多折点回归模型参数估计的迭代算法,研究了参数估计的渐近正态性质,同时讨论了指数平方损失函数中关键调谐参数的选择、模型中折点个数的确定方法和折线效应的检验问题等,数值模拟展示了本文所提方法的有限样本表现.

In this article,we investigate the robust parameter estimation and statistical inference of the longitudinal multi-kink regression model based on the exponential square loss function.A procedure based on local linear smoothing technique and modified Cholesky decomposition is proposed to improve the estimation efficiency of parameters,and the asymptotic normality are established under some mild conditions.Furthermore,we propose a data-driven procedure to automatically selecting the additional tuning parameter in exponential square loss function.In addition,a weighted cumulative sum type statistic for testing the existence of a kink-point,and a modified Bayesian information criterion for estimating the number of kink-points are developed.Finally,simulation studies show the finite sample performance of the proposed methods.