Generalized linear models with spatial dependence and a functional covariate

TL;DR

This paper develops a generalized functional linear model incorporating spatial dependence, enabling analysis of spatially correlated data with functional covariates, and provides asymptotic inference methods.

Contribution

It introduces a novel approach combining basis expansion, composite likelihood, and asymptotic theory for spatially dependent functional data.

Findings

Asymptotic confidence intervals for spatial dependence parameters.

Simulation studies verify the model's applicability.

Application to Midwest corn yield data demonstrates practical utility.

Abstract

We extend generalized functional linear models under independence to a situation in which a functional covariate is related to a scalar response variable that exhibits spatial dependence-a complex yet prevalent phenomenon. For estimation, we apply basis expansion and truncation for dimension reduction of the covariate process followed by a composite likelihood estimating equation to handle the spatial dependency. We establish asymptotic results for the proposed model under a repeating lattice asymptotic context, allowing us to construct a confidence interval for the spatial dependence parameter and a confidence band for the regression parameter function. A binary conditionals model with functional covariates is presented as a concrete illustration and is used in simulation studies to verify the applicability of the asymptotic inferential results. We apply the proposed model to a problem in which the objective is to relate annual corn yield in counties of states in the Midwestern United States to daily maximum temperatures from April to September in those same geographic regions. The extension to an expanding lattice context is further discussed in the supplement.