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August 1997 Asymptotic inference for near unit roots in spatial autoregression
B. B. Bhattacharyya, G. D. Richardson, L. A. Franklin
Ann. Statist. 25(4): 1709-1724 (August 1997). DOI: 10.1214/aos/1031594738

Abstract

Asymptotic inference for estimators of $(\alpha_n, \beta_n)$ in the spatial autoregressive model $Z_{ij}(n) = \alpha_n Z_{i-1, j}(n) + \beta_n Z_{i, j-1}(n) - \alpha_n \beta_n Z_{i-1, j-1}(n) + \varepsilon_{ij}$ 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.

Citation

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B. B. Bhattacharyya. G. D. Richardson. L. A. Franklin. "Asymptotic inference for near unit roots in spatial autoregression." Ann. Statist. 25 (4) 1709 - 1724, August 1997. https://doi.org/10.1214/aos/1031594738

Information

Published: August 1997
First available in Project Euclid: 9 September 2002

zbMATH: 0890.62018
MathSciNet: MR1463571
Digital Object Identifier: 10.1214/aos/1031594738

Subjects:
Primary: 62F12, 62M30
Secondary: 60F17

Rights: Copyright © 1997 Institute of Mathematical Statistics

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Vol.25 • No. 4 • August 1997
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