On a class of minimum contrast estimators for Gegenbauer random fields

TL;DR

This paper develops and analyzes minimum contrast estimators for Gegenbauer-based spatial long-range dependent models, establishing their consistency and asymptotic normality with supporting numerical evidence.

Contribution

It introduces a new class of estimators for Gegenbauer random fields and provides a methodology to verify their statistical properties.

Findings

Establishes consistency of the estimators.

Proves asymptotic normality of the estimators.

Numerical results confirm theoretical properties.

Abstract

The article introduces spatial long-range dependent models based on the fractional difference operators associated with the Gegenbauer polynomials. The results on consistency and asymptotic normality of a class of minimum contrast estimators of long-range dependence parameters of the models are obtained. A methodology to verify assumptions for consistency and asymptotic normality of minimum contrast estimators is developed. Numerical results are presented to confirm the theoretical findings.