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Projection expectile regression for sufficient dimension reduction

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  • Soale, Abdul-Nasah

Abstract

Many existing sufficient dimension reduction methods are designed for regression with predictors that are elliptically distributed, which limits their application in real data analyses. Projection expectile regression (PER) is proposed as a new linear sufficient dimension reduction method for handling complex predictor structures, which includes continuous, discrete, and mixed predictor variables. PER requires the link function between the response and the predictor to be monotone, but not necessarily smooth, which makes it suitable for handling stratified response surfaces. By design, PER does not involve matrix inversion or high-dimensional smoothing. Thus, PER is ideal for controlling problems associated with multicollinearity, high dimensionality, and sparsity in the predictor. An extensive simulation study demonstrates the performance of projection expectile regression in synthetic data. A real data analysis of health insurance charges in the United States is also provided. The asymptotic properties of the PER estimator are included as well.

Suggested Citation

  • Soale, Abdul-Nasah, 2023. "Projection expectile regression for sufficient dimension reduction," Computational Statistics & Data Analysis, Elsevier, vol. 180(C).
    • Handle: RePEc:eee:csdana:v:180:y:2023:i:c:s0167947322002468
    DOI: 10.1016/j.csda.2022.107666
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    References listed on IDEAS

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    1. Abdul-Nasah Soale & Yuexiao Dong, 2022. "On sufficient dimension reduction via principal asymmetric least squares," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 34(1), pages 77-94, January.
    2. Yingcun Xia & Howell Tong & W. K. Li & Li‐Xing Zhu, 2002. "An adaptive estimation of dimension reduction space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 363-410, August.
    3. Wang, Hansheng & Xia, Yingcun, 2008. "Sliced Regression for Dimension Reduction," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 811-821, June.
    4. Bierens, Herman J., 1982. "Consistent model specification tests," Journal of Econometrics, Elsevier, vol. 20(1), pages 105-134, October.
    5. Eaton, Morris L., 1986. "A characterization of spherical distributions," Journal of Multivariate Analysis, Elsevier, vol. 20(2), pages 272-276, December.
    6. Li, Bing & Wang, Shaoli, 2007. "On Directional Regression for Dimension Reduction," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 997-1008, September.
    7. Wang, Qin & Yao, Weixin, 2012. "An adaptive estimation of MAVE," Journal of Multivariate Analysis, Elsevier, vol. 104(1), pages 88-100, February.
    8. Xueqin Wang & Wenliang Pan & Wenhao Hu & Yuan Tian & Heping Zhang, 2015. "Conditional Distance Correlation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1726-1734, December.
    9. Newey, Whitney K & Powell, James L, 1987. "Asymmetric Least Squares Estimation and Testing," Econometrica, Econometric Society, vol. 55(4), pages 819-847, July.
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