The Consistency of s² in the Linear Regression Model When the Disturbances are Spatially Correlated (original) (raw)

2007

Abstract

: Conditions for the consistency of the estimator s 2 of the variance of the disturbance oe 2 u under first-order spatial error processes are given. Key words: Ordinary least squares, Consistency, Spatial error process, Spatial correlation. 1 Introduction Consider the linear regression model for spatial correlation y = Xfi + u ; u = C ffl ; (1) where y is a T \Theta 1 observable random vector, X is a T \Theta k matrix of known constants with full column rank k, fi is a k \Theta 1 vector of unknown parameters, ffl is a T \Theta 1 random vector with expectation zero and covariance matrix Cov(ffl) = oe 2 ffl I (I is the T -dimensional identity matrix and oe 2 ffl an unknown positive scalar). C denotes a T \Theta T matrix such that the product CC 0 is positive definite and has identical diagonal elements. The ordinary least squares (OLS) estimator of the unknown parameter fi in model (1) is given by fi = (X 0 X) \Gamma1 X 0 y with the covariance matrix Cov( fi) = oe ...

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