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A robust spatial autoregressive scalar-on-function regression with t-distribution

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Abstract

Modelling functional data in the presence of spatial dependence is of great practical importance as exemplified by applications in the fields of demography, economy and geography, and has received much attention recently. However, for the classical scalar-on-function regression (SoFR) with functional covariates and scalar responses, only a relatively few literature is dedicated to this relevant area, which merits further research. We propose a robust spatial autoregressive scalar-on-function regression by incorporating a spatial autoregressive parameter and a spatial weight matrix into the SoFR to accommodate spatial dependencies among individuals. The t-distribution assumption for the error terms makes our model more robust than the classical spatial autoregressive models under normal distributions. We estimate the model by firstly projecting the functional predictor onto a functional space spanned by an orthonormal functional basis and then presenting an expectation–maximization algorithm. Simulation studies show that our estimators are efficient, and are superior in the scenario with spatial correlation and heavy tailed error terms. A real weather dataset demonstrates the superiority of our model to the SoFR in the case of spatial dependence.

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Authors and Affiliations

  1. School of Economics and Management, Beihang University, Xueyuan Road No. 37,Haidian District, Beijing, China

    Tingting Huang, Huiwen Wang & Shanshan Wang

  2. Beijing Key Laboratory of Emergence Support Simulation Technologies for City Operations, Beijing, China

    Tingting Huang & Shanshan Wang

  3. CEDRIC CNAM, 292 rue St Martin, 75141, Paris Cedex 03, France

    Gilbert Saporta

  4. Beijing Advanced Innovation Center for Big Data and Brain Computing, Beihang University, Beijing, China

    Huiwen Wang

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  1. Tingting Huang
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  2. Gilbert Saporta
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  3. Huiwen Wang
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  4. Shanshan Wang
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Correspondence to Shanshan Wang.

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This research was financially supported by the National Natural Science Foundation of China under Grant Nos. 71420107025 and 11701023.

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Huang, T., Saporta, G., Wang, H. et al. A robust spatial autoregressive scalar-on-function regression with t-distribution. Adv Data Anal Classif 15, 57–81 (2021). https://doi.org/10.1007/s11634-020-00384-w

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  • DOI: https://doi.org/10.1007/s11634-020-00384-w

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