The kth Power Expectile Estimation and Testing  

作　　者：Fuming Lin Yingying Jiang Yong Zhou 

机构地区：[1]College of Mathematics and Statistics,Sichuan University of Science and Engineering,Zigong,Sichuan,People’s Republic of China [2]South Sichuan Center for Applied Mathematics,Zigong,Sichuan,People’s Republic of China [3]Key Laboratory of Advanced Theory and Application in Statistics and Data Science,MOE,and Academy of Statistics and Interdisciplinary Sciences and School of Statistics,East China Normal University,Shanghai,People’s Republic of China

出　　处：《Communications in Mathematics and Statistics》2024年第4期573-615,共43页数学与统计通讯（英文）

摘　　要：This paper develops the theory of the kth power expectile estimation and considers its relevant hypothesis tests for coefficients of linear regression models.We prove that the asymptotic covariance matrix of kth power expectile regression converges to that of quantile regression as k converges to one and hence promise a moment estimator of asymptotic matrix of quantile regression.The kth power expectile regression is then utilized to test for homoskedasticity and conditional symmetry of the data.Detailed comparisons of the local power among the kth power expectile regression tests,the quantile regression test,and the expectile regression test have been provided.When the underlying distribution is not standard normal,results show that the optimal k are often larger than 1 and smaller than 2,which suggests the general kth power expectile regression is necessary.Finally,the methods are illustrated by a real example.

关 键 词：The kth power expectiles Expectiles QUANTILES Testing for homoskedasticity Testing for conditional symmetry Estimating asymptotic matrix of quantile regression 

分 类 号：O17[理学—数学]