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

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)) is an element of N-2, 2D-RCAR(p(1), p(2)) for short. We first develop a maximum likelihood estimation procedure for estimating the unknown parameters of 2D-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.

Automated summary

This article presents new theoretical results on estimation in nonlinear random field models. The authors focus on a two dimensionally indexed random coefficients autoregressive model and develop a maximum likelihood estimation procedure for estimating the unknown parameters. The authors also prove the strong consistency of the estimates. The results are applied to construct efficient estimates in a specific model.