IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v39y2024i4d10.1007_s00180-023-01435-4.html
   My bibliography  Save this article

A new bandwidth selection method for nonparametric modal regression based on generalized hyperbolic distributions

Author

Listed:
  • Hongpeng Yuan

    (Zhejiang University of Finance and Economics)

  • Sijia Xiang

    (Zhejiang University of Finance and Economics)

  • Weixin Yao

    (University of California)

Abstract

As a complement to standard mean and quantile regression, nonparametric modal regression has been broadly applied in various fields. By focusing on the most likely conditional value of Y given x, the nonparametric modal regression is shown to be resistant to outliers and some forms of measurement error, and the prediction intervals are shorter when data is skewed. However, the bandwidth selection is critical but very challenging, since the traditional least-squares based cross-validation method cannot be applied. We propose to select the bandwidth by applying the asymptotic global optimal bandwidth and the flexible generalized hyperbolic (GH) distribution as the distribution of the error. Unlike the plug-in method, the new method does not require preliminary parameters to be chosen in advance, is easy to compute by any statistical software, and is computationally efficient compared to the existing kernel density estimator (KDE) based method. Numerical studies show that the GH based bandwidth performs better than existing bandwidth selector, in terms of higher coverage probabilities. Real data applications also illustrate the superior performance of the new bandwidth.

Suggested Citation

  • Hongpeng Yuan & Sijia Xiang & Weixin Yao, 2024. "A new bandwidth selection method for nonparametric modal regression based on generalized hyperbolic distributions," Computational Statistics, Springer, vol. 39(4), pages 1729-1746, June.
    • Handle: RePEc:spr:compst:v:39:y:2024:i:4:d:10.1007_s00180-023-01435-4
    DOI: 10.1007/s00180-023-01435-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00180-023-01435-4
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00180-023-01435-4?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. Ullah, Aman & Wang, Tao & Yao, Weixin, 2023. "Semiparametric partially linear varying coefficient modal regression," Journal of Econometrics, Elsevier, vol. 235(2), pages 1001-1026.
    2. Aman Ullah & Tao Wang & Weixin Yao, 2022. "Nonlinear modal regression for dependent data with application for predicting COVID‐19," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(3), pages 1424-1453, July.
    3. Aman Ullah & Tao Wang & Weixin Yao, 2021. "Modal regression for fixed effects panel data," Empirical Economics, Springer, vol. 60(1), pages 261-308, January.
    4. Jerome M. Krief, 2017. "Semi‐linear mode regression," Econometrics Journal, Royal Economic Society, vol. 20(2), pages 149-167, June.
    5. Morris, Katherine & McNicholas, Paul D., 2016. "Clustering, classification, discriminant analysis, and dimension reduction via generalized hyperbolic mixtures," Computational Statistics & Data Analysis, Elsevier, vol. 97(C), pages 133-150.
    6. Lee, Myoung-jae, 1993. "Quadratic mode regression," Journal of Econometrics, Elsevier, vol. 57(1-3), pages 1-19.
    7. Sun, Yiguo & Li, Qi, 2011. "Data-Driven Bandwidth Selection for Nonstationary Semiparametric Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(4), pages 541-551.
    8. Chen, Xirong & Gao, Wenzheng & Li, Zheng, 2018. "A data-driven bandwidth selection method for the smoothed maximum score estimator," Economics Letters, Elsevier, vol. 170(C), pages 24-26.
    9. Kirkby, J. Lars & Leitao, Álvaro & Nguyen, Duy, 2021. "Nonparametric density estimation and bandwidth selection with B-spline bases: A novel Galerkin method," Computational Statistics & Data Analysis, Elsevier, vol. 159(C).
    10. Weixin Yao & Bruce Lindsay & Runze Li, 2012. "Local modal regression," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(3), pages 647-663.
    11. Kemp, Gordon C.R. & Santos Silva, J.M.C., 2012. "Regression towards the mode," Journal of Econometrics, Elsevier, vol. 170(1), pages 92-101.
    12. Sijia Xiang & Weixin Yao, 2018. "Semiparametric mixtures of nonparametric regressions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(1), pages 131-154, February.
    13. Jerome M. Krief, 2017. "Semi‐linear mode regression," Econometrics Journal, Royal Economic Society, vol. 20(2), pages 149-167.
    14. Weixin Yao & Longhai Li, 2014. "A New Regression Model: Modal Linear Regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(3), pages 656-671, September.
    15. M.‐J. Lee & H. Kim, 1998. "Semiparametric econometric estimators for a truncated regression model: a review with an extension," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 52(2), pages 200-225, June.
    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. Ullah, Aman & Wang, Tao & Yao, Weixin, 2023. "Semiparametric partially linear varying coefficient modal regression," Journal of Econometrics, Elsevier, vol. 235(2), pages 1001-1026.
    2. Zhe Sun & Yundong Tu, 2024. "Factors in Fashion: Factor Analysis towards the Mode," Papers 2409.19287, arXiv.org.
    3. Aman Ullah & Tao Wang & Weixin Yao, 2022. "Nonlinear modal regression for dependent data with application for predicting COVID‐19," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(3), pages 1424-1453, July.
    4. Tao Wang, 2024. "Nonlinear kernel mode‐based regression for dependent data," Journal of Time Series Analysis, Wiley Blackwell, vol. 45(2), pages 189-213, March.
    5. Yen-Chi Chen, 2017. "Modal Regression using Kernel Density Estimation: a Review," Papers 1710.07004, arXiv.org, revised Dec 2017.
    6. Aman Ullah & Tao Wang & Weixin Yao, 2021. "Modal regression for fixed effects panel data," Empirical Economics, Springer, vol. 60(1), pages 261-308, January.
    7. Tao Wang, 2024. "Non‐parametric Estimator for Conditional Mode with Parametric Features," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 86(1), pages 44-73, February.
    8. Lianqiang Yang & Wanli Yuan & Shijie Wang, 2025. "Modal regression models based on B-splines," Computational Statistics, Springer, vol. 40(1), pages 225-248, January.
    9. Kemp, Gordon C.R. & Santos Silva, J.M.C., 2012. "Regression towards the mode," Journal of Econometrics, Elsevier, vol. 170(1), pages 92-101.
    10. Yue Chao & Lei Huang & Xuejun Ma & Jiajun Sun, 2024. "Optimal subsampling for modal regression in massive data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 87(4), pages 379-409, May.
    11. Baldauf, Markus & Santos Silva, J.M.C., 2012. "On the use of robust regression in econometrics," Economics Letters, Elsevier, vol. 114(1), pages 124-127.
    12. Gordon C. R. Kemp & Paulo M. D. C. Parente & J. M. C. Santos Silva, 2020. "Dynamic Vector Mode Regression," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(3), pages 647-661, July.
    13. repec:esx:essedp:761 is not listed on IDEAS
    14. Jales, Hugo & Jiang, Boqian & Rosenthal, Stuart S., 2023. "JUE Insight: Using the mode to test for selection in city size wage premia," Journal of Urban Economics, Elsevier, vol. 133(C).
    15. Andrés Muñoz & Daniela Rodriguez, 2023. "Robust estimation in partially nonlinear models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(5), pages 1407-1437, December.
    16. Shi, Jianhong & Zhang, Yujing & Yu, Ping & Song, Weixing, 2021. "SIMEX estimation in parametric modal regression with measurement error," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).
    17. Eduardo Schirmer Finn & Eduardo Horta, 2024. "Convolution Mode Regression," Papers 2412.05736, arXiv.org.
    18. Yang, Jing & Tian, Guoliang & Lu, Fang & Lu, Xuewen, 2020. "Single-index modal regression via outer product gradients," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    19. Hu Yang & Ning Li & Jing Yang, 2020. "A robust and efficient estimation and variable selection method for partially linear models with large-dimensional covariates," Statistical Papers, Springer, vol. 61(5), pages 1911-1937, October.
    20. Ho, Chi-san & Damien, Paul & Walker, Stephen, 2017. "Bayesian mode regression using mixtures of triangular densities," Journal of Econometrics, Elsevier, vol. 197(2), pages 273-283.
    21. Liu, Jicai & Zhang, Riquan & Zhao, Weihua & Lv, Yazhao, 2013. "A robust and efficient estimation method for single index models," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 226-238.

    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:spr:compst:v:39:y:2024:i:4:d:10.1007_s00180-023-01435-4. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.