稀疏函数型回归模型变量选择及实证分析

Variable Selection for Sparse Functional Regression Model and an Empirical Analysis

传统函数型回归模型变量选择方法,忽略了对稀疏函数型数据的讨论.提出了稀疏函数型数据情形下函数型回归模型的变量选择方法,基于条件期望对稀疏函数型自变量进行函数型主成分分析,并以估计的正交特征函数作为基函数对模型进行展开.这种方法可以有效解决对稀疏函数型变量的选择.作为实证分析,选取2002年到2011年全国34个气象观测站的年降水量,月度平均气温,光照时长,湿度,最高气温和最低气温数据,分别比较讨论了密集和稀疏情形下,原始样本和Bootstrap样本的函数型回归模型变量选择的结果,结果显示新方法具有较好的选择效果.

The traditional variable selection methods for functional regression ignore the discussion of sparse functional data.This paper proposes the variable selection methods for the case of sparse functional regression.We attempt to make functional principal analysis for the sparse functional independent variable through conditional expectation,We make the basis function expansion for the model by the estimation of orthogonal eigenfunction.This method can solve the problem of sparse functional variable selection.As the empirical analysis,we select data of 34 weather stations from 2002 to 2012：the annual total precipitation,monthly observed average temperature,time of daylight,average humidity,maximum temperature and minimum temperature.We make a discussion respectively for the result of variable selection methods for functional regression under the dense condition and sparse condition for full sample and bootstrap samples.The result display our method has a good selection result.