期刊名称：International Journal of Statistics and Probability
印刷版ISSN：1927-7032
电子版ISSN：1927-7040
出版年度：2017
卷号：6
期号：4
页码：31
DOI：10.5539/ijsp.v6n4p31
出版社：Canadian Center of Science and Education
摘要：Simultaneous spatial autoregressive model is widely used for spatial data analysis, observed at a set of grid points in a space. However a problem, not so well known, is that there exists no unique model unlike time series AR model for given autocovariances or spectral density. We show that such a non-identifiability of the model implies existence of multiple maximum likelihood estimates under Gaussianity and causes non-estimability of parameters and the singularity of Fisher information matrix. Several types of necessary and sufficient conditions for the singularity are given.
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