IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v131y2019icp80-90.html
   My bibliography  Save this article

Gaussian process methods for nonparametric functional regression with mixed predictors

Author

Listed:
  • Wang, Bo
  • Xu, Aiping

Abstract

Gaussian process methods are proposed for nonparametric functional regression for both scalar and functional responses with mixed multidimensional functional and scalar predictors. The proposed models allow the response variables to depend on the entire trajectories of the functional predictors. They inherit the desirable properties of Gaussian process regression, and can naturally accommodate both scalar and functional variables as the predictors, as well as easy to obtain and express uncertainty in predictions. The numerical experiments show that the proposed methods significantly outperform the competing models, and their usefulness is also demonstrated by the application to two real datasets.

Suggested Citation

  • Wang, Bo & Xu, Aiping, 2019. "Gaussian process methods for nonparametric functional regression with mixed predictors," Computational Statistics & Data Analysis, Elsevier, vol. 131(C), pages 80-90.
    • Handle: RePEc:eee:csdana:v:131:y:2019:i:c:p:80-90
    DOI: 10.1016/j.csda.2018.07.009
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947318301750
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2018.07.009?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. Bo Wang & Jian Qing Shi, 2014. "Generalized Gaussian Process Regression Model for Non-Gaussian Functional Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1123-1133, September.
    2. Müller, Hans-Georg & Yao, Fang, 2008. "Functional Additive Models," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1534-1544.
    3. Ferraty, F. & Van Keilegom, I. & Vieu, P., 2012. "Regression when both response and predictor are functions," Journal of Multivariate Analysis, Elsevier, vol. 109(C), pages 10-28.
    4. Ferraty, F. & Van Keilegom, Ingrid & Vieu, P., 2012. "Regression when both response and predictor are functions," LIDAM Reprints ISBA 2012004, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    5. Fang Yao & Hans-Georg Müller, 2010. "Functional quadratic regression," Biometrika, Biometrika Trust, vol. 97(1), pages 49-64.
    6. J. Q. Shi & B. Wang & R. Murray-Smith & D. M. Titterington, 2007. "Gaussian Process Functional Regression Modeling for Batch Data," Biometrics, The International Biometric Society, vol. 63(3), pages 714-723, September.
    7. Andrada Ivanescu & Ana-Maria Staicu & Fabian Scheipl & Sonja Greven, 2015. "Penalized function-on-function regression," Computational Statistics, Springer, vol. 30(2), pages 539-568, June.
    8. Guanqun Cao & Lijian Yang & David Todem, 2012. "Simultaneous inference for the mean function based on dense functional data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(2), pages 359-377.
    9. Hans-Georg Müller & Yichao Wu & Fang Yao, 2013. "Continuously additive models for nonlinear functional regression," Biometrika, Biometrika Trust, vol. 100(3), pages 607-622.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Szarek, Dawid & Maraj-Zygmąt, Katarzyna & Sikora, Grzegorz & Krapf, Diego & Wyłomańska, Agnieszka, 2022. "Statistical test for anomalous diffusion based on empirical anomaly measure for Gaussian processes," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    2. Sandra De Iaco & Donato Posa & Claudia Cappello & Sabrina Maggio, 2021. "On Some Characteristics of Gaussian Covariance Functions," International Statistical Review, International Statistical Institute, vol. 89(1), pages 36-53, April.

    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. 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.
    2. Ufuk Beyaztas & Han Lin Shang, 2021. "A partial least squares approach for function-on-function interaction regression," Computational Statistics, Springer, vol. 36(2), pages 911-939, June.
    3. Zhou, Zhiyang, 2021. "Fast implementation of partial least squares for function-on-function regression," Journal of Multivariate Analysis, Elsevier, vol. 185(C).
    4. Kehui Chen & Xiaoke Zhang & Alexander Petersen & Hans-Georg Müller, 2017. "Quantifying Infinite-Dimensional Data: Functional Data Analysis in Action," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 9(2), pages 582-604, December.
    5. Maistre, Samuel & Patilea, Valentin, 2020. "Testing for the significance of functional covariates," Journal of Multivariate Analysis, Elsevier, vol. 179(C).
    6. Goldsmith, Jeff & Scheipl, Fabian, 2014. "Estimator selection and combination in scalar-on-function regression," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 362-372.
    7. Chiou, Jeng-Min & Yang, Ya-Fang & Chen, Yu-Ting, 2016. "Multivariate functional linear regression and prediction," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 301-312.
    8. Fabio Centofanti & Antonio Lepore & Alessandra Menafoglio & Biagio Palumbo & Simone Vantini, 2023. "Adaptive smoothing spline estimator for the function-on-function linear regression model," Computational Statistics, Springer, vol. 38(1), pages 191-216, March.
    9. Shuzhi Zhu & Peixin Zhao, 2019. "Tests for the linear hypothesis in semi-functional partial linear regression models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(2), pages 125-148, March.
    10. Tingting Huang & Gilbert Saporta & Huiwen Wang & Shanshan Wang, 2021. "A robust spatial autoregressive scalar-on-function regression with t-distribution," 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. 15(1), pages 57-81, March.
    11. Andrada Ivanescu & Ana-Maria Staicu & Fabian Scheipl & Sonja Greven, 2015. "Penalized function-on-function regression," Computational Statistics, Springer, vol. 30(2), pages 539-568, June.
    12. Eduardo García‐Portugués & Javier Álvarez‐Liébana & Gonzalo Álvarez‐Pérez & Wenceslao González‐Manteiga, 2021. "A goodness‐of‐fit test for the functional linear model with functional response," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(2), pages 502-528, June.
    13. Joydeep Chowdhury & Probal Chaudhuri, 2020. "Convergence rates for kernel regression in infinite-dimensional spaces," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(2), pages 471-509, April.
    14. Zhiyong Zhou & Zhengyan Lin, 2016. "Asymptotic normality of locally modelled regression estimator for functional data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(1), pages 116-131, March.
    15. Ismail Shah & Francesco Lisi, 2020. "Forecasting of electricity price through a functional prediction of sale and purchase curves," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 39(2), pages 242-259, March.
    16. Vieu, Philippe, 2018. "On dimension reduction models for functional data," Statistics & Probability Letters, Elsevier, vol. 136(C), pages 134-138.
    17. Heungsun Hwang & Hye Suk & Yoshio Takane & Jang-Han Lee & Jooseop Lim, 2015. "Generalized Functional Extended Redundancy Analysis," Psychometrika, Springer;The Psychometric Society, vol. 80(1), pages 101-125, March.
    18. M. D. Ruiz-Medina & D. Miranda & R. M. Espejo, 2019. "Dynamical multiple regression in function spaces, under kernel regressors, with ARH(1) errors," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(3), pages 943-968, September.
    19. Ruiz-Medina, María D. & Álvarez-Liébana, Javier, 2019. "Strongly consistent autoregressive predictors in abstract Banach spaces," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 186-201.
    20. Yousri Slaoui, 2021. "Recursive non-parametric kernel classification rule estimation for independent functional data," Computational Statistics, Springer, vol. 36(1), pages 79-112, 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:csdana:v:131:y:2019:i:c:p:80-90. 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.