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Quantile Regression under Local Misspecification
Duan, Xiao-gang1; Wang, Qi-hua2
AbstractThe frequentist model averaging (FMA) and the focus information criterion (FIC) under a local framework have been extensively studied in the likelihood and regression setting since the seminal work of Hjort and Claeskens in 2003. One inconvenience, however, of the existing works is that they usually require the involved criterion function to be twice differentiable which thus prevents a direct application to the case of quantile regression (QR). This as well as some other intrinsic merits of QR motivate us to study the FIC and FMA in a locally misspecified linear QR model. Specifically, we derive in this paper the explicit asymptotic risk expression for a general submodel-based QR estimator of a focus parameter. Then based on this asymptotic result, we develop the FIC and FMA in the current setting. Our theoretical development depends crucially on the convexity of the objective function, which makes possible to establish the asymptotics based on the existing convex stochastic process theory. Simulation studies are presented to illustrate the finite sample performance of the proposed method. The low birth weight data set is analyzed.
Keywordfrequentist model averaging focus information criterion local framework quantile regression
Indexed BySCI
Funding ProjectNational Natural Science Foundation of China[11771049]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000602869700002
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Document Type期刊论文
Corresponding AuthorDuan, Xiao-gang
Affiliation1.Beijing Normal Univ, Sch Stat, Beijing 100875, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Duan, Xiao-gang,Wang, Qi-hua. Quantile Regression under Local Misspecification[J]. ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES,2020,36(4):790-802.
APA Duan, Xiao-gang,&Wang, Qi-hua.(2020).Quantile Regression under Local Misspecification.ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES,36(4),790-802.
MLA Duan, Xiao-gang,et al."Quantile Regression under Local Misspecification".ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES 36.4(2020):790-802.
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