Mercurial > octave
view scripts/statistics/gls.m @ 1315:611d403c7f3d
[project @ 1995-06-25 19:56:32 by jwe]
author | jwe |
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date | Sun, 25 Jun 1995 19:56:32 +0000 |
parents | 3f257ab07921 |
children | 5d29638dd524 |
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# Copyright (C) 1994, 1995 John W. Eaton # # This file is part of Octave. # # Octave is free software; you can redistribute it and/or modify it # under the terms of the GNU General Public License as published by the # Free Software Foundation; either version 2, or (at your option) any # later version. # # Octave is distributed in the hope that it will be useful, but WITHOUT # ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or # FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License # for more details. # # You should have received a copy of the GNU General Public License # along with Octave; see the file COPYING. If not, write to the Free # Software Foundation, 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. function [BETA, v, R] = gls (Y, X, O) # usage: [BETA, v [,R]] = gls (Y, X, O) # # Generalized Least Squares (GLS) estimation for the multivariate model # # Y = X*B + E, mean(E) = 0, cov(vec(E)) = (s^2)*O # # with Y ... T x p As usual, each row of Y and X is an observation # X ... T x k and each column a variable. # B ... k x p # E ... T x p # O ... Tp x Tp. # # BETA is the GLS estimator for B. # v is the GLS estimator for s^2. # R = Y - X*BETA is the matrix of GLS residuals. # Written by Teresa Twaroch (twaroch@ci.tuwien.ac.at) May 1993. # Dept of Probability Theory and Statistics TU Wien, Austria. if (nargin != 3) usage ("[BETA, v [, R]] = gls (Y, X, O)"); endif [rx, cx] = size (X); [ry, cy] = size (Y); if (rx != ry) error ("gls: incorrect matrix dimensions"); endif O = O^(-1/2); Z = kron (eye (cy), X); Z = O * Z; Y1 = O * reshape (Y, ry*cy, 1); U = Z' * Z; r = rank (U); if (r == cx*cy) B = inv (U) * Z' * Y1; else B = pinv (Z) * Y1; endif BETA = reshape (B, cx, cy); R = Y - X * BETA; v = (reshape (R, ry*cy, 1))' * (O^2) * reshape (R, ry*cy, 1) / (rx*cy - r); endfunction