Spatial autoregression model: strong consistency

    Authors

    B. B. Bhattacharyya; J. J. Ren; G. D. Richardson;J. Zhang

    Comments

    Authors: contact us about adding a copy of your work at STARS@ucf.edu

    Abbreviated Journal Title

    Stat. Probab. Lett.

    Keywords

    spatial autoregression; unit roots; two-parameter martingale; Statistics & Probability

    Abstract

    Let (alpha(n), beta(n)) denote the Gauss-Newton estimator of the parameter (alpha, beta) in the autoregression model Z(ij) = alphaZ(i-1,j) + betaZ(i,j-1) - alphabetaZ(i-1),(j-1) + epsilon(ij). It is shown in an earlier paper that when alpha = beta = 1, {n(3/2)(alpha(n)-alpha, beta(n)-beta)} converges in distribution to a bivariate normal random vector. A two-parameter strong martingale convergence theorem is employed here to prove that n(r)(alpha(n)-alpha, beta(n)-beta) -- > (0) under bar almost surely when r < (3)/(2). (C) 2003 Published by Elsevier B.V.

    Journal Title

    Statistics & Probability Letters

    Volume

    65

    Issue/Number

    2

    Publication Date

    1-1-2003

    Document Type

    Article

    Language

    English

    First Page

    71

    Last Page

    77

    WOS Identifier

    WOS:000186624200001

    ISSN

    0167-7152

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