On the asymptotic joint distribution of sample space--time covariance estimators

TL;DR

This paper investigates the asymptotic joint distribution of sample space-time covariance estimators for stationary random fields under mild conditions, covering various sampling schemes, with simulation validation.

Contribution

It provides a comprehensive theoretical analysis of the joint distribution of covariance estimators without strong distributional assumptions, considering different sampling scenarios.

Findings

Asymptotic joint distribution derived under mild conditions

Results hold for both regular and irregular sampling

Simulation confirms theoretical predictions

Abstract

We study the asymptotic joint distribution of sample space--time covariance estimators of strictly stationary random fields. We do this without any marginal or joint distributional assumptions other than mild moment and mixing conditions. We consider several situations depending on whether the observations are regularly or irregularly spaced and whether one part or the whole domain of interest is fixed or increasing. A simulation experiment illustrates the theoretical results.