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            <title xml:lang="en">A robust spatial autoregressive scalar-on-function regression with t-distribution</title>
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                <forename type="first">Tingting</forename>
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                <title level="j">Advances in Data Analysis and Classification</title>
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                <term xml:lang="en">Functional linear model</term>
                <term xml:lang="en">Spatial autoregressive model</term>
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              <p>Modelling functional data in the presence of spatial dependence is of great practicalimportance as exemplified by applications in the fields of demography, economyand geography, and has received much attention recently. However, for the classicalscalar-on-function regression (SoFR) with functional covariates and scalar responses,only a relatively few literature is dedicated to this relevant area, which merits furtherresearch. We propose a robust spatial autoregressive scalar-on-function regression byincorporating a spatial autoregressive parameter and a spatial weight matrix into theSoFR to accommodate spatial dependencies among individuals. The t-distributionassumption for the error terms makes our model more robust than the classical spatialautoregressive models under normal distributions. We estimate the model by firstlyprojecting the functional predictor onto a functional space spanned by an orthonormalfunctional basis and then presenting an expectation–maximization algorithm. Simulationstudies show that our estimators are efficient, and are superior in the scenario withspatial correlation and heavy tailed error terms. A real weather dataset demonstratesthe superiority of our model to the SoFR in the case of spatial dependence.</p>
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