M-estimation for near unit roots in spatial autoregression with infinite variance

Abstract

We investigate the limiting behaviour of M-estimators of parameters for a near unit root spatial autoregressive model Z _ij (n)=α _n Z _{i−1, j} (n)+β _n Z _{i, j−1}(n)−α _n β _n Z _{i−1, j−1}(n)+ε _ij , 1≤i, j≤n. Innovations are assumed to be independent and identically distributed and in the domain of attraction of a stable law. We let α _n =e ^c/n and β _n =e ^d/n , where c and d are nonzero unknown constants. It is shown that the self-normalized M-estimators are asymptotically normal. A simulation study is also given.

Keywords:

• spatial autoregression
• stable process
• M-estimates
• Itô integral

AMS 2000 Subject Classification :

• Primary 62M30
• 62M10
• secondary 62F12

Acknowledgements

This paper is supported by the Natural Sciences and Engineering Research Council of Canada.