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.
Package: stk