Suppose we have to estimate the parameters of the regression
Y(s) = b X(s) + w(s) + e
with s a set of spatial coordinates, e uncorrelated error terms and w(s) = N(0,C) where C is the covariance matrix that we assume only depends on the distance between two observations d: Cij decreases with dij. The GLS estimate of b is then
b.hat = (X C^(-1) X^T)^-1 X^T C^(-1) y
where X^T is the transpose of X and C^(-1) the inverse of C or precision matrix. My question is how can we interpret the weights C^(-1) in the estimation? Is is correct to say that more weight is given to observations that are more distant?
