IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v198y2023ics0047259x23000726.html
   My bibliography  Save this article

Gaussian copula function-on-scalar regression in reproducing kernel Hilbert space

Author

Listed:
  • Xie, Haihan
  • Kong, Linglong

Abstract

To relax the linear assumption in function-on-scalar regression, we borrow the strength of copula and propose a novel Gaussian copula function-on-scalar regression. Our model is more flexible to characterize the dynamic relationship between functional response and scalar predictors. Estimation, prediction, and inference are fully investigated. We develop a closed form for the estimator of coefficient functions in a reproducing kernel Hilbert space without the knowledge of marginal transformations. Valid, distribution-free, finite-sample prediction bands are constructed via conformal prediction. Theoretically, we establish the optimal convergence rate on the estimation of coefficient functions and show that our proposed estimator is rate-optimal under fixed and random designs. The finite-sample performance is investigated through simulations and illustrated in real data analysis.

Suggested Citation

  • Xie, Haihan & Kong, Linglong, 2023. "Gaussian copula function-on-scalar regression in reproducing kernel Hilbert space," Journal of Multivariate Analysis, Elsevier, vol. 198(C).
    • Handle: RePEc:eee:jmvana:v:198:y:2023:i:c:s0047259x23000726
    DOI: 10.1016/j.jmva.2023.105226
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X23000726
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2023.105226?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. Reiss Philip T. & Huang Lei & Mennes Maarten, 2010. "Fast Function-on-Scalar Regression with Penalized Basis Expansions," The International Journal of Biostatistics, De Gruyter, vol. 6(1), pages 1-30, August.
    2. Hojin Yang & Veerabhadran Baladandayuthapani & Arvind U.K. Rao & Jeffrey S. Morris, 2020. "Quantile Function on Scalar Regression Analysis for Distributional Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(529), pages 90-106, January.
    3. Fan, Zhaohu & Reimherr, Matthew, 2017. "High-dimensional adaptive function-on-scalar regression," Econometrics and Statistics, Elsevier, vol. 1(C), pages 167-183.
    4. Jing Lei & Max G’Sell & Alessandro Rinaldo & Ryan J. Tibshirani & Larry Wasserman, 2018. "Distribution-Free Predictive Inference for Regression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(523), pages 1094-1111, July.
    5. Jing Lei & Larry Wasserman, 2014. "Distribution-free prediction bands for non-parametric regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(1), pages 71-96, January.
    6. Yao, Fang & Muller, Hans-Georg & Wang, Jane-Ling, 2005. "Functional Data Analysis for Sparse Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 577-590, June.
    7. Xinchao Luo & Lixing Zhu & Hongtu Zhu, 2016. "Single‐index varying coefficient model for functional responses," Biometrics, The International Biometric Society, vol. 72(4), pages 1275-1284, December.
    8. Jing Lei & James Robins & Larry Wasserman, 2013. "Distribution-Free Prediction Sets," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(501), pages 278-287, March.
    9. Hyndman, Rob J. & Shahid Ullah, Md., 2007. "Robust forecasting of mortality and fertility rates: A functional data approach," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4942-4956, June.
    10. Xiaoke Zhang & Jane-Ling Wang, 2015. "Varying-coefficient additive models for functional data," Biometrika, Biometrika Trust, vol. 102(1), pages 15-32.
    11. Zhengwu Zhang & Xiao Wang & Linglong Kong & Hongtu Zhu, 2022. "High-Dimensional Spatial Quantile Function-on-Scalar Regression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 117(539), pages 1563-1578, September.
    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. Ghosal, Rahul & Ghosh, Sujit & Urbanek, Jacek & Schrack, Jennifer A. & Zipunnikov, Vadim, 2023. "Shape-constrained estimation in functional regression with Bernstein polynomials," Computational Statistics & Data Analysis, Elsevier, vol. 178(C).
    2. Victor Chernozhukov & Kaspar Wuthrich & Yinchu Zhu, 2019. "Distributional conformal prediction," Papers 1909.07889, arXiv.org, revised Aug 2021.
    3. Hu, Jianming & Luo, Qingxi & Tang, Jingwei & Heng, Jiani & Deng, Yuwen, 2022. "Conformalized temporal convolutional quantile regression networks for wind power interval forecasting," Energy, Elsevier, vol. 248(C).
    4. Diquigiovanni, Jacopo & Fontana, Matteo & Vantini, Simone, 2022. "Conformal prediction bands for multivariate functional data," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    5. Rahul Ghosal & Arnab Maity, 2023. "Variable selection in nonlinear function‐on‐scalar regression," Biometrics, The International Biometric Society, vol. 79(1), pages 292-303, March.
    6. Zhang, Xiaoke & Zhong, Qixian & Wang, Jane-Ling, 2020. "A new approach to varying-coefficient additive models with longitudinal covariates," Computational Statistics & Data Analysis, Elsevier, vol. 145(C).
    7. Li, Yehua & Qiu, Yumou & Xu, Yuhang, 2022. "From multivariate to functional data analysis: Fundamentals, recent developments, and emerging areas," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    8. Boente, Graciela & Parada, Daniela, 2023. "Robust estimation for functional quadratic regression models," Computational Statistics & Data Analysis, Elsevier, vol. 187(C).
    9. Leying Guan, 2023. "Localized conformal prediction: a generalized inference framework for conformal prediction," Biometrika, Biometrika Trust, vol. 110(1), pages 33-50.
    10. Mirshani, Ardalan & Reimherr, Matthew, 2021. "Adaptive function-on-scalar regression with a smoothing elastic net," Journal of Multivariate Analysis, Elsevier, vol. 185(C).
    11. Cees Diks & Bram Wouters, 2023. "Noise reduction for functional time series," Papers 2307.02154, arXiv.org.
    12. João A. Bastos, 2023. "Conformal prediction of option prices," Working Papers REM 2023/0304, ISEG - Lisbon School of Economics and Management, REM, Universidade de Lisboa.
    13. Han Lin Shang & Yang Yang, 2021. "Forecasting Australian subnational age-specific mortality rates," Journal of Population Research, Springer, vol. 38(1), pages 1-24, March.
    14. Ruiyan Luo & Xin Qi, 2023. "Nonlinear function‐on‐scalar regression via functional universal approximation," Biometrics, The International Biometric Society, vol. 79(4), pages 3319-3331, December.
    15. Han Lin Shang & Jiguo Cao & Peijun Sang, 2022. "Stopping time detection of wood panel compression: A functional time‐series approach," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(5), pages 1205-1224, November.
    16. Shang, Han Lin, 2013. "Bayesian bandwidth estimation for a nonparametric functional regression model with unknown error density," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 185-198.
    17. Jeff Goldsmith & Vadim Zipunnikov & Jennifer Schrack, 2015. "Generalized multilevel function-on-scalar regression and principal component analysis," Biometrics, The International Biometric Society, vol. 71(2), pages 344-353, June.
    18. Luke Durell & J. Thad Scott & Douglas Nychka & Amanda S. Hering, 2023. "Functional forecasting of dissolved oxygen in high‐frequency vertical lake profiles," Environmetrics, John Wiley & Sons, Ltd., vol. 34(4), June.
    19. Antonio Elías & Raúl Jiménez & J. E. Yukich, 2023. "Localization processes for functional data analysis," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 17(2), pages 485-517, June.
    20. Yuan Gao & Han Lin Shang, 2017. "Multivariate Functional Time Series Forecasting: Application to Age-Specific Mortality Rates," Risks, MDPI, vol. 5(2), pages 1-18, March.

    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:jmvana:v:198:y:2023:i:c:s0047259x23000726. 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/wps/find/journaldescription.cws_home/622892/description#description .

    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.