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

Amel Saidi, Abdelghani Hamaz and Ouerdia Arezki

Communications in Statistics - Theory and Methods, 2024, vol. 53, issue 1, 294-309

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 (p1,p2)∈N2, 2D−RCAR(p1,p2) for short. We first develop a maximum likelihood estimation procedure for estimating the unknown parameters of 2D−RCAR(p1,p2). 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.

Date: 2024
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DOI: 10.1080/03610926.2022.2077962

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