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Efficient information-based quantile regression model tuning with heteroscedastic errors
Journal of the Korean Data & Information Science Society 2021;32:917-29
Published online September 30, 2021;  https://doi.org/10.7465/jkdi.2021.32.5.917
© 2021 Korean Data and Information Science Society.

Wooyoung Shin1 · Yoonsuh Jung2

12Department of Statistics, Korea University
Correspondence to: 1 Graduate student, Department of Statistics, Korea University, 145 Anam-ro,Seongbuk-gu, Seoul 02841, Korea.
2 Corresponding Author: Associate professor, Department of Statistics, Korea University, 145 Anam-ro, Seongbuk-gu, Seoul 02841, Korea. E-mail: yoons77@korea.ac.kr
This work was partially supported by a Korea University Grant (K2009201) and the National Research
Received June 24, 2021; Revised July 24, 2021; Accepted August 2, 2021.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We propose a class of methods for the tuning parameter selection in quantile regression model when the errors are heteroscedastic. Check loss function is commonly used for quantile regression in model fitting and model (or tuning parameter) selection. As we are interested in the tuning parameter selection, we always use check loss function for the model fitting process. Information-based criteria are widely used for model selection, but it does not consider heteroscedastic errors. To attack this issue, we suggest using different weights in the information-based criteria. Specifically, we estimate the variation in the response variable using interquartile range (IQR). IQR is then utilized to yield weight for each sample. The effect of the samples in the high variation is expected to reduce due to the proposed method. The form of the proposed method changes depending on whether the model is linear or nonlinear. Its effectiveness for treating the heteroscedasticity is presented via simulated data and two real data sets.
Keywords : Check loss, GCV, heteroscedasticity, model selection, quantile regression, tuning parameter selection.