Missing Data in Space-time: Long Gaps Imputation Based On Functional Data Analysis

High dimensional data with spatio-temporal structures are of great interest in manyelds of research, but their exhibited complexity leads to practical issues when formulatingstatistical models. Functional data analysis through smoothing methodsis a proper framework for incorporating space-time structures: extending the basicmethodology to the multivariate spatio-temporal setting, we refer to GeneralizedAdditive Models for estimating functional data taking the spatial and temporaldependences into account, and to Functional Principal Component Analysis as aclassical dimension reduction technique to cope with the high dimensionality andwith the number of estimated eects. Since spatial and temporal dependences integrateinformation of dierent types and from dierent sources, this framework servesas synthesis of information and give important opportunities for data processing andanalysis, including extremely eective dimension reduction and estimation of missingvalues. The idea behind is to work with an estimated variance function, representedin terms of the bases and parameters dened in the estimation process, by mean ofwhich the variability is espressed in terms of the main temporal and spatial eects;the functional principal component analysis provides dimensions reduction, determiningthe uncorrelated linear combinations of the original variables that accountfor most of the variability expressed by the variance function. The eigenfunctions, orprincipal component functions, also represent an orthonormal functions set, whichcan be used to ll gaps in incomplete data: we explore the performance of imputationprocedures based on Functional Data Analysis and Empirical Orthogonal Functionapproaches when missing values, and mainly long gaps, are present in the originaldata set. In order to compare and validate the proposed procedures, a simulationplan is carried out and some performance indicators are computed under dierentmissing value patterns and in presence of long gaps.