Abstract
Quantile regression has received a great deal of attention as an important tool for modeling statistical quantities of interest other than the conditional mean. Varying coefficient models are widely used to explore dynamic patterns among popular models available to avoid the curse of dimensionality. We propose a support vector quantile regression model with varying coefficients and its two estimation methods. One uses the quadratic programming, and the other uses the iteratively reweighted least squares procedure. The proposed method can be applied easily and effectively to estimating the nonlinear regression quantiles depending on the high-dimensional vector of smoothing variables. We also present the model selection method that employs generalized cross validation and generalized approximate cross validation techniques for choosing the hyperparameters, which affect the performance of the proposed model. Numerical studies are conducted to illustrate the performance of the proposed model.
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Acknowledgments
The authors wish to thank two anonymous reviewers for their valuable and constructive comments on an earlier version of this article. The research of J. Shim was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology with Grant No. (NRF-2015R1D1A1A01056582). The research of C. Hwang was was supported by the Human Resources Program in Energy Technology of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) granted financial resource from the Ministry of Trade, Industry & Energy, Republic of Korea (No. 20154030200830), and the research of K. Seok was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology with Grant No. (2011-0009705).
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Shim, J., Hwang, C. & Seok, K. Support vector quantile regression with varying coefficients. Comput Stat 31, 1015–1030 (2016). https://doi.org/10.1007/s00180-016-0647-5
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DOI: https://doi.org/10.1007/s00180-016-0647-5