Asymptotic inference for near unit roots in spatial autoregression

    Authors

    B. B. Bhattacharyya; G. D. Richardson;L. A. Franklin

    Comments

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    Abbreviated Journal Title

    Ann. Stat.

    Keywords

    spatial autoregressive process; near unit roots; Gauss-Newton; estimation; central limit theory; CENTRAL LIMIT THEOREMS; LATTICE PROCESSES; TIME-SERIES; MODELS; PLANE; Statistics & Probability

    Abstract

    Asymptotic inference for estimators of (alpha(n), beta(n)) in the spatial autoregressive model Z(ij)(n)= alpha(n)Z(i-1,j)(n) + beta(n)Z(i,j-1)(n) - alpha(n) beta(n)Z(i-1,j-1)(n) + epsilon(ij) is Obtained when alpha(n) and beta(n) are near unit roots. When alpha(n) and beta(n) are reparameterized by alpha(n) = e(c/n) and beta(n) = e(d/n), it is shown that if the "one-step Gauss-Newton estimator" of lambda(1)alpha(n) + lambda(2)beta(n) is properly normalized and embedded in the function space D([0, 1](2)), the limiting distribution is a Gaussian process. The key idea in the proof relies on a maximal inequality for a two-parameter martingale which may be of independent interest. A simulation study illustrates the speed of convergence and goodness-of-fit of these estimators for various sample sizes.

    Journal Title

    Annals of Statistics

    Volume

    25

    Issue/Number

    4

    Publication Date

    1-1-1997

    Document Type

    Article

    Language

    English

    First Page

    1709

    Last Page

    1724

    WOS Identifier

    WOS:A1997YB69000014

    ISSN

    0090-5364

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