One-dimensional Nonstationary Process Variance Function Estimation

TL;DR

This paper introduces a difference-based method for estimating the variance function of one-dimensional nonstationary spatial processes, effectively handling correlated errors and outperforming likelihood-based approaches in accuracy and efficiency.

Contribution

It proposes a novel difference-based estimation technique with a bandwidth selection method tailored for nonstationary, correlated errors in one-dimensional processes.

Findings

Lower integrated MSE compared to local-likelihood methods

Effectively fixes boundary bias issues

Requires less computational time

Abstract

Many spatial processes exhibit nonstationary features. We estimate a variance function from a single process observation where the errors are nonstationary and correlated. We propose a difference-based approach for a one-dimensional nonstationary process and develop a bandwidth selection method for smoothing, taking into account the correlation in the errors. The estimation results are compared to that of a local-likelihood approach proposed by Anderes and Stein(2011). A simulation study shows that our method has a smaller integrated MSE, easily fixes the boundary bias problem, and requires far less computing time than the likelihood-based method.