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Simultaneous estimation and factor selection in quantile regression via adaptive sup-norm regularization

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  • Bang, Sungwan
  • Jhun, Myoungshic

Abstract

Some regularization methods, including the group lasso and the adaptive group lasso, have been developed for the automatic selection of grouped variables (factors) in conditional mean regression. In many practical situations, such a problem arises naturally when a set of dummy variables is used to represent a categorical factor and/or when a set of basis functions of a continuous variable is included in the predictor set. Complementary to these earlier works, the simultaneous and automatic factor selection is examined in quantile regression. To incorporate the factor information into regularized model fitting, the adaptive sup-norm regularized quantile regression is proposed, which penalizes the empirical check loss function by the sum of factor-wise adaptive sup-norm penalties. It is shown that the proposed method possesses the oracle property. A simulation study demonstrates that the proposed method is a more appropriate tool for factor selection than the adaptive lasso regularized quantile regression.

Suggested Citation

  • Bang, Sungwan & Jhun, Myoungshic, 2012. "Simultaneous estimation and factor selection in quantile regression via adaptive sup-norm regularization," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 813-826.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:4:p:813-826
    DOI: 10.1016/j.csda.2011.01.026
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    3. Y. Andriyana & I. Gijbels & A. Verhasselt, 2014. "P-splines quantile regression estimation in varying coefficient models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(1), pages 153-194, March.
    4. Shiyi Tu & Min Wang & Xiaoqian Sun, 2017. "Bayesian variable selection and estimation in maximum entropy quantile regression," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(2), pages 253-269, January.

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