Simulating mixed regressive spatially autoregressive estimators (Q1297865)

A spatial autoregressive error process is considered for which holds \[ y=X\beta +(I-\alpha D)^{-1}\varepsilon, \] where \(y\) is the \(n\)-dimensional vector of the dependent variable observations, \(X\) is the matrix of independent variables values, \(\beta\) is a vector of unknown parameters, \(\varepsilon\) is the vector of i.i.d. normal errors, \(D\) is an \(n\times n\) matrix specifying the spatial lag structure. A positive entry \(D_{ij}\) of \(D\) indicates that the \(j\)-th observation affects the \(i\)-th observation (\(i\not=j\)). It is supposed that \(D_{ij}\geq 0\), \(D_{ii}=0\), \(\sum_jD_{ij}=1\). The parameter \(\alpha\) (\(0\leq \alpha<1\)) is unknown. Least squares and maximum likelihood estimators for \(\beta\) and \(\alpha\) are described. The authors propose to use sparse matrices \(D\), e.g., considering only the interaction between nearest neighbors. This greatly accelerates computations. Monte Carlo experiment results are described.