STK_PARAM_GLS computes a generalised least squares estimate
CALL: BETA = stk_param_gls (MODEL, XI, ZI)
computes a generalised least squares estimate BETA of the vector of
coefficients for the linear part of MODEL, where XI and ZI stand for
the evaluation points and observed responses, respectively.
CALL: [BETA, SIGMA2] = stk_param_gls (MODEL, XI, ZI)
also returns the associated unbiased estimate SIGMA2 of sigma^2, assu-
ming that the actual covariance matrix of the Gaussian process part of
the model is sigma^2 K, with K the covariance matrix built from MODEL.
SIGMA2 is actually the "best" unbiased estimate of sigma^2 :
1
SIGMA2 = ----- * || ZI - P BETA ||^2_{K^{-1}}
n - r
where n is the number of observations, r the length of BETA, P the
design matrix for the linear part of the model, and || . ||_{K^{-1}}
the norm associated to the positive definite matrix K^{-1}. It is the
best estimate with respect to the quadratic risk, among all unbiased
estimates which are quadratic in the residuals.