Book Sections Year : 2021

Quasi-maximum Likelihood Estimators for Functional Linear Spatial Autoregressive Models

Mohamed-Salem Ahmed
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Laurence Broze
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Abstract

A functional linear autoregressive spatial model, where the explanatory variable takes values in a function space, while the response process is real-valued and spatially autocorrelated, is proposed. The specificity of the model is due to the functional nature of the explanatory variable and the structure of a spatial weight matrix that defines the spatial dependency between neighbors. The estimation procedure consists of reducing the infinite dimension of the functional explanatory variable and maximizing the quasi-maximum likelihood. We establish the consistency and asymptotic normality of the estimator. The ability of the methodology is illustrated via simulations and by application to real data.
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Dates and versions

hal-01810819 , version 1 (08-06-2018)

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Mohamed-Salem Ahmed, Laurence Broze, Sophie Dabo-Niang, Zied Gharbi. Quasi-maximum Likelihood Estimators for Functional Linear Spatial Autoregressive Models. Ramon Giraldo; Jorge Mateu. Geostatistical Functional Data Analysis: Theory and Methods, Wiley, 2021, Wiley Series in Probability and Statistics, 978-1-119-38784-8. ⟨10.1002/9781119387916.ch12⟩. ⟨hal-01810819⟩
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