IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i10p1785-d822169.html
   My bibliography  Save this article

On Robustness for Spatio-Temporal Data

Author

Listed:
  • Alfonso García-Pérez

    (Departamento de Estadística, I.O. y C.N., Universidad Nacional de Educación a Distancia (UNED), Senda del Rey 9, 28040 Madrid, Spain)

Abstract

The spatio-temporal variogram is an important factor in spatio-temporal prediction through kriging, especially in fields such as environmental sustainability or climate change, where spatio-temporal data analysis is based on this concept. However, the traditional spatio-temporal variogram estimator, which is commonly employed for these purposes, is extremely sensitive to outliers. We approach this problem in two ways in the paper. First, new robust spatio-temporal variogram estimators are introduced, which are defined as M -estimators of an original data transformation. Second, we compare the classical estimate against a robust one, identifying spatio-temporal outliers in this way. To accomplish this, we use a multivariate scale-contaminated normal model to produce reliable approximations for the sample distribution of these new estimators. In addition, we define and study a new class of M -estimators in this paper, including real-world applications, in order to determine whether there are any significant differences in the spatio-temporal variogram between two temporal lags and, if so, whether we can reduce the number of lags considered in the spatio-temporal analysis.

Suggested Citation

  • Alfonso García-Pérez, 2022. "On Robustness for Spatio-Temporal Data," Mathematics, MDPI, vol. 10(10), pages 1-17, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:10:p:1785-:d:822169
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/10/1785/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/10/1785/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Ronchetti, Elvezio, 2020. "Accurate and robust inference," Econometrics and Statistics, Elsevier, vol. 14(C), pages 74-88.
    2. La Vecchia, Davide & Ronchetti, Elvezio, 2019. "Saddlepoint approximations for short and long memory time series: A frequency domain approach," Journal of Econometrics, Elsevier, vol. 213(2), pages 578-592.
    3. Bruno Ebner & Norbert Henze, 2020. "Tests for multivariate normality—a critical review with emphasis on weighted $$L^2$$ L 2 -statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(4), pages 845-892, December.
    4. Bruno Ebner & Norbert Henze, 2020. "Rejoinder on: Tests for multivariate normality—a critical review with emphasis on weighted $$L^2$$ L 2 -statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(4), pages 911-913, December.
    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. Alfonso García-Pérez, 2021. "New Robust Cross-Variogram Estimators and Approximations of Their Distributions Based on Saddlepoint Techniques," Mathematics, MDPI, vol. 9(7), pages 1-21, April.
    2. Wanfang Chen & Marc G. Genton, 2023. "Are You All Normal? It Depends!," International Statistical Review, International Statistical Institute, vol. 91(1), pages 114-139, April.
    3. Jurgita Arnastauskaitė & Tomas Ruzgas & Mindaugas Bražėnas, 2021. "A New Goodness of Fit Test for Multivariate Normality and Comparative Simulation Study," Mathematics, MDPI, vol. 9(23), pages 1-20, November.
    4. Chen, Feifei & Jiménez–Gamero, M. Dolores & Meintanis, Simos & Zhu, Lixing, 2022. "A general Monte Carlo method for multivariate goodness–of–fit testing applied to elliptical families," Computational Statistics & Data Analysis, Elsevier, vol. 175(C).
    5. Alfonso García-Pérez, 2023. "A New Estimator: Median of the Distribution of the Mean in Robustness," Mathematics, MDPI, vol. 11(12), pages 1-13, June.
    6. Chaonan Jiang & Davide La Vecchia & Elvezio Ronchetti & Olivier Scaillet, 2023. "Saddlepoint Approximations for Spatial Panel Data Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 118(542), pages 1164-1175, April.
    7. Ronchetti, Elvezio, 2020. "Accurate and robust inference," Econometrics and Statistics, Elsevier, vol. 14(C), pages 74-88.

    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:gam:jmathe:v:10:y:2022:i:10:p:1785-:d:822169. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.