Nonparametric regression of spatio-temporal data using infinite-dimensional covariates

2026-04-02

AI Summary

This study addresses the challenges posed by potentially infinite-dimensional covariates and non-mixing dependence structures in spatiotemporal data by proposing a nonparametric regression framework conditioned on second-order stationary covariates. The work innovatively replaces conventional mixing assumptions with a polynomially decaying moment contraction (PMC) condition, enabling effective modeling of infinite-dimensional spatiotemporal covariates. Employing kernel estimation techniques, the authors establish statistical consistency of the mean function estimator under the PMC condition and construct simultaneous confidence intervals based on a central limit theorem. Comprehensive theoretical analysis, simulation studies, and applications to two real-world datasets demonstrate that the proposed method exhibits strong finite-sample performance and is suitable for hypothesis testing regarding the functional form of the mean.

Abstract

In spatio-temporal analysis, we often record data at specific time intervals but with varying spatial locations between these timepoints. We propose a conditional model to analyze such spatio-temporal data that accommodates the dependencies alongside second-order stationary explanatory variables, which may be infinite-dimensional and accommodate spatio-temporal covariates. Because of the absence of a mixing-type dependence condition in this case, which is typically required by the existing studies, we consider a weaker polynomially decaying moment contraction (PMC) condition on the covariates. In this paper, we obtain nonparametric point estimates of the mean and covariate functions of such a regression model, which we then show to be statistically consistent. We also obtain a simultaneous confidence interval of the mean function using the central limit theorem for the proposed estimator. Such simultaneous inference tools can be used to test for certain specifications of the mean function. Some simulation studies and two real-data analyses have been illustrated to corroborate the findings.

Problem

• spatio-temporal data
• nonparametric regression
• infinite-dimensional covariates
• statistical consistency
• simultaneous inference

Innovation

• nonparametric regression
• spatio-temporal data
• infinite-dimensional covariates
• polynomially decaying moment contraction
• simultaneous confidence interval