IJPAM: Volume 15, No. 4 (2004)

PARAMETER ESTIMATION IN A NONSTATIONARY
SPATIAL AUTOREGRESSION MODEL

B.B. Bhattacharyya$^1$, G. Richardson$^2$, J. Zhang$^3$
$^1$Department of Statistics
North Carolina State University
Raleigh, NC 27695-8203, USA
$^{2,3}$Department of Mathematics
University of Central Florida
P.O. Box 161364, Orlando, FL 32816-1364, USA
$^2$e-mail: garyr@pegasus.cc.ucf.edu


Abstract.The limiting distribution for Gauss-Newton estimators of $(\al ,\be )$ in the model $Z_{ij}=\al Z_{i-1,j}+\be Z_{i,j-1}-\al\be Z_{i-1,j-1}+\ep_{ij}$ is obtained for the case when $\al =1$ and $\vert\be\vert>1$. The asymptotic distribution is shown to be a Gaussian process when the estimators are appropriately embedded in $D([0,1]^2)$. Results given here differ significantly from the earlier cases studied.

Received: June 14, 2004

AMS Subject Classification: 62F12, 62M30, 60F17

Key Words and Phrases: nonstationary processes, Gauss-Newton estimation,
$D([0,1]^2)$

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2004
Volume: 15
Issue: 4