带有自相关结构误差的多元函数型回归模型的变量选择

Variable Selection in Multiple Functional Regression Model with Autoregressive Errors

多元函数型回归模型是经典多元线性模型的有益扩展.本文研究带有自相关结构误差的多元函数型回归模型的变量选择.我们基于Group SCAD(smoothly clipped absolute deviation)惩罚研究了模型中函数型协变量的变量选择和误差项的自相关阶数的确定问题.此外,我们在一定的正则性条件下证明了估计量的选择相合性和渐近正态性,并通过数值模拟说明提出方法在有限样本下具有良好性质.

Multiple functional regression models are a useful extension of classical multiple linear model.This paper focuses on the variable selection of multiple functional regression models with autoregressive errors.Based on Group SCAD(Smoothly Clipped Absolute Deviation)penalty,we study the variable selection of functional covariates and the order of the autoregressive error term simultaneously.In addition,we provide the selection consistency and asymptotic normality under mild conditions,and demonstrate its performance through simulation studies.