Estimation in nonlinear random fields models of autoregressive type with random parameters

Abstract

In this article, we present new original theoretical results on estimation in nonlinear random field models. We focus on two dimensionally indexed random coefficients autoregressive model with order $(p_1,p_2)\in {\mathbb{N}}^2, 2D-\mathit{RCAR}(p_1,p_2)$ for short. We first develop a maximum likelihood estimation procedure for estimating the unknown parameters of $2D-\mathit{RCAR}(p_1,p_2).$ Moreover, we prove that the estimates are strongly consistent. Finally, these results are then applied to construct efficient estimates in 2D-RCAR model of order (0, 1). Then, a simulation part is given to illustrate the effectiveness and accuracy of the estimates.

Keywords:

• 2D-RCAR models
• nonlinear random fields
• maximum likelihood
• strong consistency

Acknowledgments

We are deeply indebted to Pr. BIBI Abdelouahab of the University of Oum El Bouaghi for his guidance on the subject matter.

Correction Statement

This article has been corrected with minor changes. These changes do not impact the academic content of the article.

Additional information

Funding

The authors thank the General Directorate of Scientific Research and Technological Development (DGRSDT/MESRS-Algeria) for their financial support.