diff doc/interpreter/optim.txi @ 3368:a4cd1e9d9962

[project @ 1999-11-20 17:22:48 by jwe]
author jwe
date Sat, 20 Nov 1999 17:23:01 +0000
parents bfe1573bd2ae
children aae05d51353c
line wrap: on
line diff
--- a/doc/interpreter/optim.txi	Sat Nov 20 14:52:42 1999 +0000
+++ b/doc/interpreter/optim.txi	Sat Nov 20 17:23:01 1999 +0000
@@ -28,101 +28,6 @@
 @node Linear Least Squares,  , Nonlinear Programming, Optimization
 @section Linear Least Squares
 
-@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
-@ifinfo
-@code{@var{y} = @var{x} * @var{b} + @var{e}} with @code{mean (@var{e}) =
-0} and @code{cov (vec (@var{e})) = (@var{s}^2)*@var{o}},
-@end ifinfo
- 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
-@ifinfo
-@var{Y} is a @var{T} by @var{p} matrix, @var{X} is a @var{T} by @var{k}
-matrix, @var{B} is a @var{k} by @var{p} matrix, @var{E} is a @var{T} by
-@var{p} matrix, and @var{O} is a @var{T}@var{p} by @var{T}@var{p}
-matrix.
-@end ifinfo
-
-@noindent
-Each row of Y and 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 @var{b}.
-
-@item v
-The GLS estimator for @code{@var{s}^2}.
-
-@item r
-The matrix of GLS residuals, @code{@var{r} = @var{y} - @var{x} *
-@var{beta}}.
-@end table
-@end deftypefn
+@DOCSTRING(gls)
 
-@deftypefn {Function File} {[@var{beta}, @var{sigma}, @var{r}] =} ols (@var{y}, @var{x})
-Ordinary least squares estimation for the multivariate model
-@iftex
-@tex
-$y = x b + e$
-with
-$\bar{e} = 0$, and cov(vec($e$)) = kron ($s, I$)
-@end tex
-@end iftex
-@ifinfo
-@code{@var{y} = @var{x}*@var{b} + @var{e}} with
-@code{mean (@var{e}) = 0} and @code{cov (vec (@var{e})) = kron (@var{s},
-@var{I})}.
-@end ifinfo
- where
-@iftex
-@tex
-$y$ is a $t \times p$ matrix, $x$ is a $t \times k$ matrix, 
-$b$ is a $k \times p$ matrix, and $e$ is a $t \times p$ matrix.
-@end tex
-@end iftex
-@ifinfo
-@var{y} is a @var{t} by @var{p} matrix, @var{X} is a @var{t} by @var{k}
-matrix, @var{B} is a @var{k} by @var{p} matrix, and @var{e} is a @var{t}
-by @var{p} matrix.
-@end ifinfo
-
-Each row of @var{y} and @var{x} is an observation and each column a
-variable.
-
-The return values @var{beta}, @var{sigma}, and @var{r} are defined as
-follows.
-
-@table @var
-@item beta
-The OLS estimator for @var{b}, @code{@var{beta} = pinv (@var{x}) *
-@var{y}}, where @code{pinv (@var{x})} denotes the pseudoinverse of
-@var{x}.
-
-@item sigma
-The OLS estimator for the matrix @var{s},
-
-@example
-@group
-@var{sigma} = (@var{y}-@var{x}*@var{beta})' * (@var{y}-@var{x}*@var{beta}) / (@var{t}-rank(@var{x}))
-@end group
-@end example
-
-@item r
-The matrix of OLS residuals, @code{@var{r} = @var{y} - @var{x} * @var{beta}}.
-@end table
-@end deftypefn
+@DOCSTRING(ols)