Title

Spatial Autoregression Model: Strong Consistency

Keywords

Spatial autoregression; Two-parameter martingale; Unit roots

Abstract

Let (α̂n,β̂n) denote the Gauss-Newton estimator of the parameter (α,β) in the autoregression model Zij=α Zi-1,j+βZi,j-1-αβ Zi-1,j-1+Eij. It is shown in an earlier paper that when α=β=1, {n3/2 (α̂n-α,β̂n-β)} converges in distribution to a bivariate normal random vector. A two-parameter strong martingale convergence theorem is employed here to prove that nr(α̂n-α, β̂n-β)→0̄ almost surely when r< 3/2. © 2003 Published by Elsevier Science B.V.

Publication Date

11-1-2003

Publication Title

Statistics and Probability Letters

Volume

65

Issue

2

Number of Pages

71-77

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.spl.2003.07.004

Socpus ID

0142153219 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/0142153219

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