Consistency of modified LS estimation method for identifying 2-D noncausal SAR model parameters

Least squares (LS) and maximum likelihood (ML) are the two main methods for parameter estimation of two-dimensional (2D) noncausal simultaneous autoregressive (SAR) models. ML is asymptotically consistent and unbiased but computationally unattractive. On the other hand, conventional LS is computationally efficient but does not produce accurate parameter estimates for noncausal models. Recently, Zhao-Yu (1993) proposed a modified LS estimation method and was shown to be unbiased. In this paper we prove that, under certain assumptions, the method introduced by Zhao-Yu is also consistent