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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?

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    Does this answer your question? [What is the geometric relationship between the covariance matrix and the inverse of the covariance matrix?](https://stats.stackexchange.com/questions/464387/what-is-the-geometric-relationship-between-the-covariance-matrix-and-the-inverse) – POC Apr 13 '21 at 00:25

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