Recent developments in complex and spatially correlated functional data Article Swipe
YOU?
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· 2020
· Open Access
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· DOI: https://doi.org/10.1214/20-bjps466
· OA: W2998155358
As high-dimensional and high-frequency data are being collected on a large\nscale, the development of new statistical models is being pushed forward.\nFunctional data analysis provides the required statistical methods to deal with\nlarge-scale and complex data by assuming that data are continuous functions,\ne.g., a realization of a continuous process (curves) or continuous random\nfields (surfaces), and that each curve or surface is considered as a single\nobservation. Here, we provide an overview of functional data analysis when data\nare complex and spatially correlated. We provide definitions and estimators of\nthe first and second moments of the corresponding functional random variable.\nWe present two main approaches: The first assumes that data are realizations of\na functional random field, i.e., each observation is a curve with a spatial\ncomponent. We call them 'spatial functional data'. The second approach assumes\nthat data are continuous deterministic fields observed over time. In this case,\none observation is a surface or manifold, and we call them 'surface time\nseries'. For the two approaches, we describe software available for the\nstatistical analysis. We also present a data illustration, using a\nhigh-resolution wind speed simulated dataset, as an example of the two\napproaches. The functional data approach offers a new paradigm of data\nanalysis, where the continuous processes or random fields are considered as a\nsingle entity. We consider this approach to be very valuable in the context of\nbig data.\n
