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Inference for spatial regression models with functional response using a permutational approach

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  • Římalová, Veronika
  • Fišerová, Eva
  • Menafoglio, Alessandra
  • Pini, Alessia

Abstract

The aim of this work is to introduce an approach to null hypothesis significance testing in a functional linear model for spatial data. The proposed method is capable of dealing with the spatial structure of data by building a permutation testing procedure on spatially filtered residuals of a spatial regression model. Indeed, due to the spatial dependence existing among the data, the residuals of the regression model are not exchangeable, breaking the basic assumptions of the Freedman and Lane permutation scheme. Instead, it is proposed here to estimate the variance–covariance structure of the residuals by variography, remove this correlation by spatial filtering residuals and base the permutation test on these approximately exchangeable residuals. A simulation study is conducted to evaluate the performance of the proposed method in terms of empirical size and power, examining its behavior under different covariance settings. We show that neglecting the residuals spatial structure in the permutation scheme (thus permuting the correlated residuals directly) yields a very liberal testing procedures, whereas the proposed procedure is close to the nominal size of the test. The methodology is demonstrated on a real world data set on the amount of waste production in the Venice province of Italy.

Suggested Citation

  • Římalová, Veronika & Fišerová, Eva & Menafoglio, Alessandra & Pini, Alessia, 2022. "Inference for spatial regression models with functional response using a permutational approach," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
  • Handle: RePEc:eee:jmvana:v:189:y:2022:i:c:s0047259x21001718
    DOI: 10.1016/j.jmva.2021.104893
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    References listed on IDEAS

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    1. Menafoglio, Alessandra & Petris, Giovanni, 2016. "Kriging for Hilbert-space valued random fields: The operatorial point of view," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 84-94.
    2. Veronika Římalová & Alessandra Menafoglio & Alessia Pini & Vilém Pechanec & Eva Fišerová, 2020. "A permutation approach to the analysis of spatiotemporal geochemical data in the presence of heteroscedasticity," Environmetrics, John Wiley & Sons, Ltd., vol. 31(4), June.
    3. Jiang Du & Ruiyuan Cao & Eddy Kwessi & Zhongzhan Zhang, 2019. "Estimation for generalized partially functional linear additive regression model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 46(5), pages 914-925, April.
    4. Menafoglio, Alessandra & Secchi, Piercesare, 2017. "Statistical analysis of complex and spatially dependent data: A review of Object Oriented Spatial Statistics," European Journal of Operational Research, Elsevier, vol. 258(2), pages 401-410.
    5. Bernardi, Mara S. & Carey, Michelle & Ramsay, James O. & Sangalli, Laura M., 2018. "Modeling spatial anisotropy via regression with partial differential regularization," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 15-30.
    6. Arnone, Eleonora & Azzimonti, Laura & Nobile, Fabio & Sangalli, Laura M., 2019. "Modeling spatially dependent functional data via regression with differential regularization," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 275-295.
    7. Elvira Romano & Jorge Mateu & Ramon Giraldo, 2015. "On the performance of two clustering methods for spatial functional data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 99(4), pages 467-492, October.
    8. Collazos, Julian A.A. & Dias, Ronaldo & Zambom, Adriano Z., 2016. "Consistent variable selection for functional regression models," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 63-71.
    9. A. Pini & S. Vantini, 2017. "Interval-wise testing for functional data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(2), pages 407-424, April.
    10. Marco Marozzi, 2002. "Some notes on nonparametric inferences and permutation tests," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3-4), pages 139-151.
    11. Ramón Giraldo & William Caballero & Jesús Camacho-Tamayo, 2018. "Mantel test for spatial functional data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 102(1), pages 21-39, January.
    12. Konrad Abramowicz & Charlotte K. Häger & Alessia Pini & Lina Schelin & Sara Sjöstedt de Luna & Simone Vantini, 2018. "Nonparametric inference for functional‐on‐scalar linear models applied to knee kinematic hop data after injury of the anterior cruciate ligament," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 45(4), pages 1036-1061, December.
    13. Zhu, Hanbing & Zhang, Riquan & Yu, Zhou & Lian, Heng & Liu, Yanghui, 2019. "Estimation and testing for partially functional linear errors-in-variables models," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 296-314.
    14. Freedman, David & Lane, David, 1983. "A Nonstochastic Interpretation of Reported Significance Levels," Journal of Business & Economic Statistics, American Statistical Association, vol. 1(4), pages 292-298, October.
    15. Aneiros, Germán & Cao, Ricardo & Fraiman, Ricardo & Genest, Christian & Vieu, Philippe, 2019. "Recent advances in functional data analysis and high-dimensional statistics," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 3-9.
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