The Correct Classic Generalized Least-Squares Estimator of an Unknown Constant Mean of Randon Field

TL;DR

This paper derives the correct classical generalized least-squares estimator for the unknown constant mean of a random field with negative correlation and a time parameter, ensuring accurate estimation asymptotically.

Contribution

It provides the asymptotic form of the generalized least-squares estimator for negatively correlated random fields with a time component, correcting previous formulations.

Findings

Derived the asymptotic form of the estimator.

Confirmed the estimator's correctness for negative correlation functions.

Enhanced understanding of estimation in temporally correlated random fields.

Abstract

The aim of the paper is to derive for the negative correlation function with a time parameter an asymptotic disjunction of the numerical generalized least-squares estimator of an unknown constant mean of random field in fact the correct classic generalized least-squares estimator of an unknown constant mean of the field.