#### Title

Asymptotic inference for near unit roots in spatial autoregression

#### 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

#### ISSN

0090-5364

#### Recommended Citation

"Asymptotic inference for near unit roots in spatial autoregression" (1997). *Faculty Bibliography 1990s*. 1858.

http://stars.library.ucf.edu/facultybib1990/1858

## Comments

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