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

TL;DR

This paper introduces a nonparametric regression method for spatio-temporal data with infinite-dimensional covariates, providing consistent estimators and confidence intervals without requiring mixing conditions.

Contribution

It develops a novel nonparametric approach for infinite-dimensional covariates in spatio-temporal models under weaker dependence assumptions.

Findings

Establishes statistical consistency of the estimators.

Provides a method for constructing simultaneous confidence intervals.

Demonstrates effectiveness through simulations and real data analyses.

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.