Asymptotic inference for near unit roots in spatial autoregression

• 成果类型: Article
• 署名作者: Bhattacharyya, BB; Richardson, GD; Franklin, LA
• 署名单位: North Carolina State University; State University System of Florida; University of Central Florida; Indiana State University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1997
• 页码: 1709-1724
• 关键词: central limit theorems; lattice processes; time-series; models; plane

摘要

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.