% -*- 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 % @tex % $y = x b + e$ % with $\bar{e} = 0$ and cov(vec($e$)) = $(s^2)o$, % @end tex % @ifnottex % @math{y = x b + e} with @math{mean (e) = 0} and % @math{cov (vec (e)) = (s^2) o}, % @end ifnottex % where % @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 % @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