IDEAS home Printed from https://ideas.repec.org/p/zbw/irtgdp/2018030.html
   My bibliography  Save this paper

Gaussian Process Forecast with multidimensional distributional entries

Author

Listed:
  • Bachoc, Francois
  • Suvorikova, Alexandra
  • Loubes, Jean-Michel
  • Spokoiny, Vladimir

Abstract

In this work, we propose to define Gaussian Processes indexed by multidimensional distributions. In the framework where the distributions can be modeled as i.i.d realizations of a measure on the set of distributions, we prove that the kernel defined as the quadratic distance between the transportation maps, that transport each distribution to the barycenter of the distributions, provides a valid covariance function. In this framework, we study the asymptotic properties of this process, proving micro ergodicity of the parameters.

Suggested Citation

  • Bachoc, Francois & Suvorikova, Alexandra & Loubes, Jean-Michel & Spokoiny, Vladimir, 2018. "Gaussian Process Forecast with multidimensional distributional entries," IRTG 1792 Discussion Papers 2018-030, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    • Handle: RePEc:zbw:irtgdp:2018030
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/230741/1/irtg1792dp2018-030.pdf
    Download Restriction: no
    ---><---

    Citations

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


    Cited by:

    1. Qingliang Fan & Wei Zhong, 2018. "Nonparametric Additive Instrumental Variable Estimator: A Group Shrinkage Estimation Perspective," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(3), pages 388-399, July.
    2. Zhong, Wei & Liu, Xi & Ma, Shuangge, 2018. "Variable selection and direction estimation for single-index models via DC-TGDR method," IRTG 1792 Discussion Papers 2018-050, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    3. Guo, Li & Tao, Yubo & Härdle, Wolfgang Karl, 2018. "Understanding Latent Group Structure of Cryptocurrencies Market: A Dynamic Network Perspective," IRTG 1792 Discussion Papers 2018-032, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    4. Packham, Natalie & Woebbeking, Fabian, 2018. "A factor-model approach for correlation scenarios and correlation stress-testing," IRTG 1792 Discussion Papers 2018-034, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    5. Xiaojia Bao & Qingliang Fan, 2020. "The impact of temperature on gaming productivity: evidence from online games," Empirical Economics, Springer, vol. 58(2), pages 835-867, February.
    6. Packham, Natalie & Kalkbrener, Michael & Overbeck, Ludger, 2018. "Default probabilities and default correlations under stress," IRTG 1792 Discussion Papers 2018-037, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    7. Kuczmaszewska, Anna & Yan, Ji Gao, 2018. "On complete convergence in Marcinkiewicz-Zygmund type SLLN for random variables," IRTG 1792 Discussion Papers 2018-041, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    8. Chen, Haiqiang & Li, Yingxing & Lin, Ming & Zhu, Yanli, 2018. "A Regime Shift Model with Nonparametric Switching Mechanism," IRTG 1792 Discussion Papers 2018-048, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    9. Yatracos, Yannis G., 2018. "Residual'S Influence Index (Rinfin), Bad Leverage And Unmasking In High Dimensional L2-Regression," IRTG 1792 Discussion Papers 2018-060, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    10. Zbonakova, Lenka & Li, Xinjue & Härdle, Wolfgang Karl, 2018. "Penalized Adaptive Forecasting with Large Information Sets and Structural Changes," IRTG 1792 Discussion Papers 2018-039, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    11. Packham, Natalie, 2018. "Optimal contracts under competition when uncertainty from adverse selection and moral hazard are present," IRTG 1792 Discussion Papers 2018-033, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    12. Cai, Zongwu & Fang, Ying & Lin, Ming & Su, Jia, 2018. "Inferences for a Partially Varying Coefficient Model With Endogenous Regressors," IRTG 1792 Discussion Papers 2018-047, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    13. Wang, Honglin & Yu, Fan & Zhou, Yinggang, 2018. "Property Investment and Rental Rate under Housing Price Uncertainty: A Real Options Approach," IRTG 1792 Discussion Papers 2018-051, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    14. Yan, Ji Gao, 2018. "Complete Convergence and Complete Moment Convergence for Maximal Weighted Sums of Extended Negatively Dependent Random Variables," IRTG 1792 Discussion Papers 2018-040, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    15. Kalkbrener, Michael & Packham, Natalie, 2018. "Correlation Under Stress In Normal Variance Mixture Models," IRTG 1792 Discussion Papers 2018-035, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    16. Chiu, Hsin-Yu & Chiang, Mi-Hsiu & Kuo, Wei-Yu, 2018. "Predicative Ability of Similarity-based Futures Trading Strategies," IRTG 1792 Discussion Papers 2018-045, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    17. Guo, Shaojun & Li, Dong & Li, Muyi, 2018. "Strict Stationarity Testing and GLAD Estimation of Double Autoregressive Models," IRTG 1792 Discussion Papers 2018-049, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".

    More about this item

    Keywords

    Gaussian Process; Kernel methods; Wasserstein Distance;
    All these keywords.

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General

    Statistics

    Access and download statistics

    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:zbw:irtgdp:2018030. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: ZBW - Leibniz Information Centre for Economics (email available below). General contact details of provider: https://edirc.repec.org/data/wfhubde.html .

    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.