A central limit theorem for a sequence of conditionally centered random fields

TL;DR

This paper proves a central limit theorem for sums of conditionally centered random fields with mixing conditions, enabling asymptotic normality results for space-time processes in statistical inference.

Contribution

It introduces a CLT for random fields with conditional centering and mixing, applicable to space-time data analysis and unbiased estimating functions.

Findings

Limiting normal distribution derived for increasing spatial and temporal domains.

Applicable to a wide range of space-time processes.

Two examples demonstrate practical relevance.

Abstract

A central limit theorem is established for a sum of random variables belonging to a sequence of random fields. The fields are assumed to have zero mean conditional on the past history and to satisfy certain conditional $\alpha$-mixing conditions in space or time. Exploiting conditional centering and the space-time structure, the limiting normal distribution is obtained for increasing spatial domain, increasing length of the sequence, or both of these. The theorem is very well suited for establishing asymptotic normality in the context of unbiased estimating function inference for a wide range of space-time processes. This is pertinent given the abundance of space-time data. Two examples demonstrate the applicability of the theorem.