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Quantile Regression under Local Misspecification

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Abstract

The 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.

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Acknowledgments

The authors appreciate the associate editor and two referees for some useful comments.

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Authors and Affiliations

  1. School of Statistics, Beijing Normal University, Beijing, 100875, China

    Xiao-gang Duan

  2. Academy of Mathematics and System Science, Chinese Academy of Sciences, Beijing, 100190, China

    Qi-hua Wang

Authors
  1. Xiao-gang Duan
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  2. Qi-hua Wang
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Correspondence to Xiao-gang Duan.

Additional information

This paper is supported by the National Natural Science Foundation of China (No. 11771049).

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Duan, Xg., Wang, Qh. Quantile Regression under Local Misspecification. Acta Math. Appl. Sin. Engl. Ser. 36, 790–802 (2020). https://doi.org/10.1007/s10255-020-0973-9

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  • DOI: https://doi.org/10.1007/s10255-020-0973-9

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