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May 2020 Recent developments in complex and spatially correlated functional data
Israel Martínez-Hernández, Marc G. Genton
Braz. J. Probab. Stat. 34(2): 204-229 (May 2020). DOI: 10.1214/20-BJPS466

Abstract

As high-dimensional and high-frequency data are being collected on a large scale, the development of new statistical models is being pushed forward. Functional data analysis provides the required statistical methods to deal with large-scale and complex data by assuming that data are continuous functions, for example, realizations of a continuous process (curves) or continuous random field (surfaces), and that each curve or surface is considered as a single observation. Here, we provide an overview of functional data analysis when data are complex and spatially correlated. We provide definitions and estimators of the first and second moments of the corresponding functional random variable. We present two main approaches: The first assumes that data are realizations of a functional random field, that is, each observation is a curve with a spatial component. We call them spatial functional data. The second approach assumes that data are continuous deterministic fields observed over time. In this case, one observation is a surface or manifold, and we call them surface time series. For these two approaches, we describe software available for the statistical analysis. We also present a data illustration, using a high-resolution wind speed simulated dataset, as an example of the two approaches. The functional data approach offers a new paradigm of data analysis, where the continuous processes or random fields are considered as a single entity. We consider this approach to be very valuable in the context of big data.

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Israel Martínez-Hernández. Marc G. Genton. "Recent developments in complex and spatially correlated functional data." Braz. J. Probab. Stat. 34 (2) 204 - 229, May 2020. https://doi.org/10.1214/20-BJPS466

Information

Received: 1 January 2020; Accepted: 1 January 2020; Published: May 2020
First available in Project Euclid: 4 May 2020

zbMATH: 07232926
MathSciNet: MR4093256
Digital Object Identifier: 10.1214/20-BJPS466

Rights: Copyright © 2020 Brazilian Statistical Association

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Vol.34 • No. 2 • May 2020
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