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Some first inferential tools for spatial regression with differential regularization

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  • Ferraccioli, Federico
  • Sangalli, Laura M.
  • Finos, Livio

Abstract

Spatial regression with differential regularization is an innovative approach at the crossroad between functional data analysis and spatial data analysis. These models have been shown to be numerically efficient and capable to handle complex applied problems. On the other hand, their theoretical properties are still largely unexplored. Here we consider the discrete estimators in spatial regression models with differential regularization, obtained after numerical discretization, using an expansion on a finite element basis. We study the consistency and the asymptotic normality of these discrete estimators. We also propose a nonparametric test procedure for the linear part of the models, based on random sign-flipping of the score components. The test exploits an appropriate decomposition of the smoothing matrix, in order to reduce the effect of the spatial dependence, without any parametric assumption on the form of the correlation structure. The proposed test is shown to be superior to parametric alternatives.

Suggested Citation

  • Ferraccioli, Federico & Sangalli, Laura M. & Finos, Livio, 2022. "Some first inferential tools for spatial regression with differential regularization," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    • Handle: RePEc:eee:jmvana:v:189:y:2022:i:c:s0047259x21001445
    DOI: 10.1016/j.jmva.2021.104866
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    1. Yu Y. & Ruppert D., 2002. "Penalized Spline Estimation for Partially Linear Single-Index Models," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1042-1054, December.
    2. Simon N. Wood, 2003. "Thin plate regression splines," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 95-114, February.
    3. B. Ettinger & S. Perotto & L. M. Sangalli, 2016. "Spatial regression models over two-dimensional manifolds," Biometrika, Biometrika Trust, vol. 103(1), pages 71-88.
    4. Cora J. M. Maas & Joop J. Hox, 2004. "Robustness issues in multilevel regression analysis," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 58(2), pages 127-137, May.
    5. Laura M. Sangalli, 2021. "Spatial Regression With Partial Differential Equation Regularisation," International Statistical Review, International Statistical Institute, vol. 89(3), pages 505-531, December.
    6. Freedman, David A., 2006. "On The So-Called "Huber-Sandwich Estimator" and "Robust Standard Errors"," The American Statistician, American Statistical Association, vol. 60, pages 299-302, November.
    7. Aldo Solari & Livio Finos & Jelle J. Goeman, 2014. "Rotation-based multiple testing in the multivariate linear model," Biometrics, The International Biometric Society, vol. 70(4), pages 954-961, December.
    8. Li, Qi, 2000. "Efficient Estimation of Additive Partially Linear Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 41(4), pages 1073-1092, November.
    9. Laura M. Sangalli & James O. Ramsay & Timothy O. Ramsay, 2013. "Spatial spline regression models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(4), pages 681-703, September.
    10. Kherad-Pajouh, Sara & Renaud, Olivier, 2010. "An exact permutation method for testing any effect in balanced and unbalanced fixed effect ANOVA," Computational Statistics & Data Analysis, Elsevier, vol. 54(7), pages 1881-1893, July.
    11. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167.
    12. Jesse Hemerik & Jelle J. Goeman, 2018. "False discovery proportion estimation by permutations: confidence for significance analysis of microarrays," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(1), pages 137-155, January.
    13. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
    14. 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.
    15. 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.
    16. Laura Azzimonti & Laura M. Sangalli & Piercesare Secchi & Maurizio Domanin & Fabio Nobile, 2015. "Blood Flow Velocity Field Estimation Via Spatial Regression With PDE Penalization," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 1057-1071, September.
    17. Simon N. Wood & Mark V. Bravington & Sharon L. Hedley, 2008. "Soap film smoothing," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(5), pages 931-955, November.
    18. Jesse Hemerik & Jelle J. Goeman & Livio Finos, 2020. "Robust testing in generalized linear models by sign flipping score contributions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(3), pages 841-864, July.
    19. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506.
    20. 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.
    21. Inyoung Kim & Noah D. Cohen & Raymond J. Carroll, 2003. "Semiparametric Regression Splines in Matched Case-Control Studies," Biometrics, The International Biometric Society, vol. 59(4), pages 1158-1169, December.
    22. Schlather, Martin & Malinowski, Alexander & Menck, Peter J. & Oesting, Marco & Strokorb, Kirstin, 2015. "Analysis, Simulation and Prediction of Multivariate Random Fields with Package RandomFields," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 63(i08).
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