Statistical inference in the partial functional linear expectile regression model  

作　　者：Juxia Xiao Ping Yu Xinyuan Song Zhongzhan Zhang 

机构地区：[1]Faculty of Science,Beijing University of Technology,Beijing 100124,China [2]School of Mathematics and Computer Science,Shanxi Normal University,Taiyuan 030092,China [3]Department of Statistics,The Chinese University of Hong Kong,Hong Kong 999077,China

出　　处：《Science China Mathematics》2022年第12期2601-2630,共30页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant No.11771032);Natural Science Foundation of Shanxi Province of China(Grant No.201901D111279);the Research Grant Council of the Hong Kong Special Administration Region(Grant Nos.14301918 and 14302519);。

摘　　要：As extensions of means, expectiles embrace all the distribution information of a random variable.The expectile regression is computationally friendlier because the asymmetric least square loss function is differentiable everywhere. This regression also enables effective estimation of the expectiles of a response variable when potential explanatory variables are given. In this study, we propose the partial functional linear expectile regression model. The slope function and constant coefficients are estimated by using the functional principal component basis. The convergence rate of the slope function and the asymptotic normality of the parameter vector are established. To inspect the effect of the parametric component on the response variable, we develop Wald-type and expectile rank score tests and establish their asymptotic properties. The finite performance of the proposed estimators and test statistics are evaluated through simulation study. Results indicate that the proposed estimators are comparable to competing estimation methods and the newly proposed expectile rank score test is useful. The methodologies are illustrated by using two real data examples.

关 键 词：expectile regression functional principal component analysis Wald-type test expectile rank score test HETEROSCEDASTICITY 

分 类 号：O212.1[理学—概率论与数理统计]