Statistical Modelling 23 (4) (2023), 327–346
Smoothing spatio-temporal data with complex missing data patterns
Eleonora Arnone,
MOX - Dipartimento di Matematica,
Politecnico di Milano,
Milano,
Italy.
Laura M Sangalli,
MOX - Dipartimento di Matematica,
Politecnico di Milano,
Milano,
Italy.
e-mail: laura.sangalli@polimi.it
Andrea Vicini,
MOX - Dipartimento di Matematica,
Politecnico di Milano,
Milano,
Italy.
Abstract:
We consider spatio-temporal data and functional data with spatial dependence,
characterized by complicated missing data patterns. We propose a new method capable to efficiently
handle these data structures, including the case where data are missing over large portions of
the spatio-temporal domain. The method is based on regression with partial differential equation
regularization. The proposed model can accurately deal with data scattered over domains with irregular
shapes and can accurately estimate fields exhibiting complicated local features. We demonstrate the
consistency and asymptotic normality of the estimators. Moreover, we illustrate the good performances
of the method in simulations studies, considering different missing data scenarios, from sparse data to
more challenging scenarios where the data are missing over large portions of the spatial and temporal
domains and the missing data are clustered in space and/or in time. The proposed method is compared
to competing techniques, considering predictive accuracy and uncertainty quantification measures.
Finally, we show an application to the analysis of lake surface water temperature data, that further
illustrates the ability of the method to handle data featuring complicated patterns of missingness and
highlights its potentiality for environmental studies.
Keywords:
Functional data with spatial dependence, incomplete and partially observed functional
data, nonparametric regression with partial differential equation regularization, smoothing with
roughness penalties
Downloads:
Data and R Code, Supplementary material.
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