The \(k\)th power expectile regression
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.
scientific article; zbMATH DE number 7382996
scientific article