IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v180y2023ics0167947322002468.html
   My bibliography  Save this article

Projection expectile regression for sufficient dimension reduction

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947322002468
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2022.107666?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. Eaton, Morris L., 1986. "A characterization of spherical distributions," Journal of Multivariate Analysis, Elsevier, vol. 20(2), pages 272-276, December.
    3. 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.
    4. 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.
    5. Wang, Qin & Yao, Weixin, 2012. "An adaptive estimation of MAVE," Journal of Multivariate Analysis, Elsevier, vol. 104(1), pages 88-100, February.
    6. 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.
    7. Newey, Whitney K & Powell, James L, 1987. "Asymmetric Least Squares Estimation and Testing," Econometrica, Econometric Society, vol. 55(4), pages 819-847, July.
    8. 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.
    9. Bierens, Herman J., 1982. "Consistent model specification tests," Journal of Econometrics, Elsevier, vol. 20(1), pages 105-134, October.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Weng, Jiaying, 2022. "Fourier transform sparse inverse regression estimators for sufficient variable selection," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    2. Wang, Pei & Yin, Xiangrong & Yuan, Qingcong & Kryscio, Richard, 2021. "Feature filter for estimating central mean subspace and its sparse solution," Computational Statistics & Data Analysis, Elsevier, vol. 163(C).
    3. Sheng, Wenhui & Yin, Xiangrong, 2013. "Direction estimation in single-index models via distance covariance," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 148-161.
    4. Ming-Yueh Huang & Chin-Tsang Chiang, 2017. "An Effective Semiparametric Estimation Approach for the Sufficient Dimension Reduction Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1296-1310, July.
    5. Kapla, Daniel & Fertl, Lukas & Bura, Efstathia, 2022. "Fusing sufficient dimension reduction with neural networks," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    6. Wang, Qin & Xue, Yuan, 2021. "An ensemble of inverse moment estimators for sufficient dimension reduction," Computational Statistics & Data Analysis, Elsevier, vol. 161(C).
    7. Lu Li & Kai Tan & Xuerong Meggie Wen & Zhou Yu, 2023. "Variable-dependent partial dimension reduction," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(2), pages 521-541, June.
    8. Moradi Rekabdarkolaee, Hossein & Wang, Qin, 2017. "Variable selection through adaptive MAVE," Statistics & Probability Letters, Elsevier, vol. 128(C), pages 44-51.
    9. Wenjuan Li & Wenying Wang & Jingsi Chen & Weidong Rao, 2023. "Aggregate Kernel Inverse Regression Estimation," Mathematics, MDPI, vol. 11(12), pages 1-10, June.
    10. Rekabdarkolaee, Hossein Moradi & Boone, Edward & Wang, Qin, 2017. "Robust estimation and variable selection in sufficient dimension reduction," Computational Statistics & Data Analysis, Elsevier, vol. 108(C), pages 146-157.
    11. Portier, François & Delyon, Bernard, 2013. "Optimal transformation: A new approach for covering the central subspace," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 84-107.
    12. Zhang, Jing & Wang, Qin & Mays, D'Arcy, 2021. "Robust MAVE through nonconvex penalized regression," Computational Statistics & Data Analysis, Elsevier, vol. 160(C).
    13. Eliana Christou, 2020. "Robust dimension reduction using sliced inverse median regression," Statistical Papers, Springer, vol. 61(5), pages 1799-1818, October.
    14. Zhang, Hong-Fan, 2021. "Minimum Average Variance Estimation with group Lasso for the multivariate response Central Mean Subspace," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    15. Zifang Guo & Lexin Li & Wenbin Lu & Bing Li, 2015. "Groupwise Dimension Reduction via Envelope Method," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1515-1527, December.
    16. Liu, Xuejing & Yu, Zhou & Wen, Xuerong Meggie & Paige, Robert, 2015. "On testing common indices for two multi-index models: A link-free approach," Journal of Multivariate Analysis, Elsevier, vol. 136(C), pages 75-85.
    17. Wen, Xuerong Meggie, 2010. "On sufficient dimension reduction for proportional censorship model with covariates," Computational Statistics & Data Analysis, Elsevier, vol. 54(8), pages 1975-1982, August.
    18. Zhao, Junlong & Zhao, Xiuli, 2010. "Dimension reduction using the generalized gradient direction," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 1089-1102, April.
    19. Wu, Runxiong & Chen, Xin, 2021. "MM algorithms for distance covariance based sufficient dimension reduction and sufficient variable selection," Computational Statistics & Data Analysis, Elsevier, vol. 155(C).
    20. Zeng, Bilin & Yu, Zhou & Wen, Xuerong Meggie, 2015. "A note on cumulative mean estimation," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 322-327.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:180:y:2023:i:c:s0167947322002468. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.