The \(k\)th power expectile regression
type: Item
instance of: scholarly article
title: The \(k\)th power expectile regression
zbMATH Open document ID: 1479.62025
author: Yingying Jiang
author: Fuming Lin
author: Yong Zhou
published in: Annals of the Institute of Statistical Mathematics
publication date: 2021-08-18T00:00:00Z
review text: For a classical linear regression model, quantile and expectile regression methods have been proposed to improve the traditional least square estimates for the regression coefficients. The estimators from these methods are obtained by minimizing a total asymmetric \(k\)th power error loss with respectively \(k=1\) and 2. More general estimators with \(1<k\leq 2\) are considered in this paper. An estimator with \(1<k<2\) would offer a compromise between the robustness with \(k=1\) and high-normal-theory efficiency with \(k=2\). Large sample properties, such as consistency and asymptotic normality, of the proposed estimators are established in this paper under some regularity conditions. A consistent variance estimator and a computing algorithm are also developed. Simulation studies are performed to compare the efficiency of the proposed estimator with the estimators obtained from quantile and expectile regression and a method is proposed to select \(k\) to gain more efficiency in applications. The proposed methods are applied to analyze the incomes of migrant workers from a survey conducted by the State Statistical Bureau of China in 2011.
Mathematics Subject Classification ID: 62G08
Mathematics Subject Classification ID: 62G20
Mathematics Subject Classification ID: 62P20
zbMATH DE Number: 7382996
zbMATH Keywords: asymptotic normality
zbMATH Keywords: consistency
zbMATH Keywords: efficiency
zbMATH Keywords: expectiles
zbMATH Keywords: quantiles
zbMATH Keywords: robustness
reviewed by: Dongsheng Tu
describes a project that uses: CAViaR
MaRDI profile type: Publication
full work available at URL: s10463-019-00738-y
OpenAlex ID: W2996294044
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DOI: 10.1007/S10463-019-00738-Y
description: scientific article; zbMATH DE number 7382996