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A goodness-of-fit test for regression models with spatially correlated errors

Author

Listed:
  • Andrea Meilán-Vila

    (Universidade da Coruña)

  • Jean D. Opsomer

    (Westat)

  • Mario Francisco-Fernández

    (Universidade da Coruña)

  • Rosa M. Crujeiras

    (Universidade de Santiago de Compostela)

Abstract

The problem of assessing a parametric regression model in the presence of spatial correlation is addressed in this work. For that purpose, a goodness-of-fit test based on a $$L_2$$ L 2 -distance comparing a parametric and nonparametric regression estimators is proposed. Asymptotic properties of the test statistic, both under the null hypothesis and under local alternatives, are derived. Additionally, a bootstrap procedure is designed to calibrate the test in practice. Finite sample performance of the test is analyzed through a simulation study, and its applicability is illustrated using a real data example.

Suggested Citation

  • Andrea Meilán-Vila & Jean D. Opsomer & Mario Francisco-Fernández & Rosa M. Crujeiras, 2020. "A goodness-of-fit test for regression models with spatially correlated errors," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(3), pages 728-749, September.
    • Handle: RePEc:spr:testjl:v:29:y:2020:i:3:d:10.1007_s11749-019-00678-y
    DOI: 10.1007/s11749-019-00678-y
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    References listed on IDEAS

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    1. Wenceslao González-Manteiga & Rosa Crujeiras, 2013. "Rejoinder on: An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 442-447, September.
    2. Bowman, Adrian W. & Crujeiras, Rosa M., 2013. "Inference for variograms," Computational Statistics & Data Analysis, Elsevier, vol. 66(C), pages 19-31.
    3. Crujeiras, Rosa M. & Van Keilegom, Ingrid, 2010. "Least squares estimation of nonlinear spatial trends," LIDAM Reprints ISBA 2010007, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. Stefanie Biedermann & Holger Dette, 2000. "Testing linearity of regression models with dependent errors by kernel based methods," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 9(2), pages 417-438, December.
    5. A. Diblasi & A. W. Bowman, 2001. "On the Use of the Variogram in Checking for Independence in Spatial Data," Biometrics, The International Biometric Society, vol. 57(1), pages 211-218, March.
    6. Wenceslao González‐Manteiga & Rosa M. Crujeiras & Mario Francisco‐Fernández & Alejandro Quintela‐del‐Río & Rubén Fernández‐Casal, 2012. "Nonparametric methods for spatial regression. An application to seismic events," Environmetrics, John Wiley & Sons, Ltd., vol. 23(1), pages 85-93, February.
    7. Wenceslao González-Manteiga & Rosa Crujeiras, 2013. "An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 361-411, September.
    8. Marc Hallin & Zudi Lu & Lanh T. Tran, 2004. "Local linear spatial regression," ULB Institutional Repository 2013/2131, ULB -- Universite Libre de Bruxelles.
    9. Biedermann, Stefanie & Dette, Holger, 2000. "Testing linearity of regression models with dependent errors by kernel based methods," Technical Reports 2000,40, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    10. Crujeiras, Rosa M. & Van Keilegom, Ingrid, 2010. "Least squares estimation of nonlinear spatial trends," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 452-465, February.
    11. Gonzalez Manteiga, W. & Vilar Fernandez, J. M., 1995. "Testing linear regression models using non-parametric regression estimators when errors are non-independent," Computational Statistics & Data Analysis, Elsevier, vol. 20(5), pages 521-541, November.
    12. J. Opsomer & M. Francisco-Fernández, 2010. "Finding local departures from a parametric model using nonparametric regression," Statistical Papers, Springer, vol. 51(1), pages 69-84, January.
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    Cited by:

    1. A. Meilán-Vila & R. Fernández-Casal & R. M. Crujeiras & M. Francisco-Fernández, 2021. "A computational validation for nonparametric assessment of spatial trends," Computational Statistics, Springer, vol. 36(4), pages 2939-2965, December.

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