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
Copyright Status
Unknown
Socpus ID
0031483681 (Scopus)
Source API URL
https://api.elsevier.com/content/abstract/scopus_id/0031483681
STARS Citation
Bhattacharyya, B. B.; Richardson, G. D.; and Franklin, L. A., "Asymptotic inference for near unit roots in spatial autoregression" (1997). Scopus Export 1990s. 2741.
https://stars.library.ucf.edu/scopus1990/2741