Spatial Functional Data analysis: Irregular spacing and Bernstein polynomials

Abstract

Spatial Functional Data (SFD) analysis is an emerging statistical framework that combines Functional Data Analysis (FDA) and spatial dependency modeling. Unlike traditional statistical methods, which treat data as scalar values or vectors, SFD considers data as continuous functions, allowing for a more comprehensive understanding of their behavior and variability. This approach is well-suited for analyzing data collected over time, space, or any other continuous domain. SFD has found applications in various fields, including economics, finance, medicine, environmental science, and engineering. This study proposes new functional Gaussian models incorporating spatial dependence structures, focusing on irregularly spaced data and reflecting spatially correlated curves. The model is based on Bernstein polynomial (BP) basis functions and utilizes a Bayesian approach for estimating unknown quantities and parameters. The paper explores the advantages and limitations of the BP model in capturing complex shapes and patterns while ensuring numerical stability. The main contributions of this work include the development of an innovative model designed for SFD using BP, the presence of a random effect to address associations between irregularly spaced observations, and a comprehensive simulation study to evaluate models’ performance under various scenarios. The work also presents one real application of Temperature in Mexico City, showcasing practical illustrations of the proposed model.