Title

Asymptotic inference for near unit roots in spatial autoregression

Keywords

Central limit theory; Gauss-Newton estimation; Near unit roots; Spatial autoregressive process

Abstract

Asymptotic inference for estimators of (αn, βn) in the spatial autoregressive model Zij(n) = αnβnZi Zi-1, j(n) + βnZi, j-1(n) - αn βnZi-1, j-1(n) + εij is obtained when αn and βn are near unit roots. When αn and βn are reparameterized by αn = ec/n and βn = ed/n, it is shown that if the "one-step Gauss-Newton estimator" of λ1αn + λ2 βn 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.

Publication Date

1-1-1997

Publication Title

Annals of Statistics

Volume

25

Issue

4

Number of Pages

1709-1724

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1214/aos/1031594738

Socpus ID

0031483681 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/0031483681

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