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## Copyright (C) 1996 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.
## usage: [BETA, SIGMA [, R]] = ols (Y, X)
##
## Ordinary Least Squares (OLS) estimation for the multivariate model
##
## Y = X*B + E, mean(E) = 0, cov(vec(E)) = kron(S,I)
##
## 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.
##
## BETA is the OLS estimator for B, i.e.
##
## BETA = pinv(X)*Y,
##
## where pinv(X) denotes the pseudoinverse of X.
## SIGMA is the OLS estimator for the matrix S, i.e.
##
## SIGMA = (Y - X*BETA)'*(Y - X*BETA) / (T - rank(X)).
##
## R = Y - X*BETA is the matrix of OLS residuals.
## Author: Teresa Twaroch <twaroch@ci.tuwien.ac.at>
## Created: May 1993
## Adapted-By: jwe
function [BETA, SIGMA, R] = ols (Y, X)
if (nargin != 2)
error("usage : [BETA, SIGMA [, R]] = ols (Y, X)");
endif
[nr, nc] = size (X);
[ry, cy] = size (Y);
if (nr != ry)
error ("ols: incorrect matrix dimensions");
endif
Z = X' * X;
r = rank (Z);
if (r == nc)
BETA = inv (Z) * X' * Y;
else
BETA = pinv (X) * Y;
endif
R = Y - X * BETA;
SIGMA = R' * R / (nr - r);
endfunction
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