Home > freetb4matlab > statistics > base > gls.m

gls

PURPOSE ^

% Generalized least squares estimation for the multivariate model

SYNOPSIS ^

function [BETA, v, R] = gls (Y, X, O)

DESCRIPTION ^

% -*- texinfo -*-
% @deftypefn {Function File} {[@var{beta}, @var{v}, @var{r}] =} gls (@var{y}, @var{x}, @var{o})
% Generalized least squares estimation for the multivariate model
% @iftex
% @tex
% $y = x b + e$
% with $\bar{e} = 0$ and cov(vec($e$)) = $(s^2)o$,
% @end tex
% @end iftex
% @ifnottex
% @math{y = x b + e} with @math{mean (e) = 0} and
% @math{cov (vec (e)) = (s^2) o},
% @end ifnottex
%  where
% @iftex
% @tex
% $y$ is a $t \times p$ matrix, $x$ is a $t \times k$ matrix, $b$ is a $k
% \times p$ matrix, $e$ is a $t \times p$ matrix, and $o$ is a $tp \times
% tp$ matrix.
% @end tex
% @end iftex
% @ifnottex
% @math{y} is a @math{t} by @math{p} matrix, @math{x} is a @math{t} by
% @math{k} matrix, @math{b} is a @math{k} by @math{p} matrix, @math{e}
% is a @math{t} by @math{p} matrix, and @math{o} is a @math{t p} by
% @math{t p} matrix.
% @end ifnottex
%
% @noindent
% Each row of @var{y} and @var{x} is an observation and each column a
% variable.  The return values @var{beta}, @var{v}, and @var{r} are
% defined as follows.
%
% @table @var
% @item beta
% The GLS estimator for @math{b}.
%
% @item v
% The GLS estimator for @math{s^2}.
%
% @item r
% The matrix of GLS residuals, @math{r = y - x beta}.
% @end table
% @end deftypefn

CROSS-REFERENCE INFORMATION ^

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