Mercurial > hg > octave-nkf
annotate scripts/statistics/base/gls.m @ 8517:81d6ab3ac93c
Allow documentation tobe built for other formats than tex and info
| author | sh@sh-laptop |
|---|---|
| date | Wed, 14 Jan 2009 20:44:25 -0500 |
| parents | a1dbe9d80eee |
| children | eb63fbe60fab |
| rev | line source |
|---|---|
| 7017 | 1 ## Copyright (C) 1996, 1997, 1998, 1999, 2000, 2005, 2006, 2007 |
| 2 ## John W. Eaton | |
| 3200 | 3 ## |
| 4 ## This file is part of Octave. | |
| 5 ## | |
| 6 ## Octave is free software; you can redistribute it and/or modify it | |
| 7 ## under the terms of the GNU General Public License as published by | |
| 7016 | 8 ## the Free Software Foundation; either version 3 of the License, or (at |
| 9 ## your option) any later version. | |
| 3200 | 10 ## |
| 11 ## Octave is distributed in the hope that it will be useful, but | |
| 12 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
| 13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
| 14 ## General Public License for more details. | |
| 15 ## | |
| 16 ## You should have received a copy of the GNU General Public License | |
| 7016 | 17 ## along with Octave; see the file COPYING. If not, see |
| 18 ## <http://www.gnu.org/licenses/>. | |
| 3200 | 19 |
| 3381 | 20 ## -*- texinfo -*- |
| 3368 | 21 ## @deftypefn {Function File} {[@var{beta}, @var{v}, @var{r}] =} gls (@var{y}, @var{x}, @var{o}) |
| 22 ## Generalized least squares estimation for the multivariate model | |
| 23 ## @iftex | |
| 24 ## @tex | |
| 25 ## $y = x b + e$ | |
| 26 ## with $\bar{e} = 0$ and cov(vec($e$)) = $(s^2)o$, | |
| 27 ## @end tex | |
| 28 ## @end iftex | |
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29 ## @ifnottex |
| 3499 | 30 ## @math{y = x b + e} with @math{mean (e) = 0} and |
| 31 ## @math{cov (vec (e)) = (s^2) o}, | |
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32 ## @end ifnottex |
| 3368 | 33 ## where |
| 34 ## @iftex | |
| 3426 | 35 ## @tex |
| 3368 | 36 ## $y$ is a $t \times p$ matrix, $x$ is a $t \times k$ matrix, $b$ is a $k |
| 37 ## \times p$ matrix, $e$ is a $t \times p$ matrix, and $o$ is a $tp \times | |
| 38 ## tp$ matrix. | |
| 39 ## @end tex | |
| 40 ## @end iftex | |
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41 ## @ifnottex |
| 3499 | 42 ## @math{y} is a @math{t} by @math{p} matrix, @math{x} is a @math{t} by |
| 43 ## @math{k} matrix, @math{b} is a @math{k} by @math{p} matrix, @math{e} | |
| 44 ## is a @math{t} by @math{p} matrix, and @math{o} is a @math{t p} by | |
| 45 ## @math{t p} matrix. | |
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changeset
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46 ## @end ifnottex |
| 3426 | 47 ## |
| 3368 | 48 ## @noindent |
| 3499 | 49 ## Each row of @var{y} and @var{x} is an observation and each column a |
| 50 ## variable. The return values @var{beta}, @var{v}, and @var{r} are | |
| 51 ## defined as follows. | |
| 3426 | 52 ## |
| 3368 | 53 ## @table @var |
| 54 ## @item beta | |
| 3499 | 55 ## The GLS estimator for @math{b}. |
| 3426 | 56 ## |
| 3368 | 57 ## @item v |
| 3499 | 58 ## The GLS estimator for @math{s^2}. |
| 3426 | 59 ## |
| 3368 | 60 ## @item r |
| 3499 | 61 ## The matrix of GLS residuals, @math{r = y - x beta}. |
| 3368 | 62 ## @end table |
| 63 ## @end deftypefn | |
| 3200 | 64 |
| 65 ## Author: Teresa Twaroch <twaroch@ci.tuwien.ac.at> | |
| 66 ## Created: May 1993 | |
| 67 ## Adapted-By: jwe | |
| 68 | |
| 69 function [BETA, v, R] = gls (Y, X, O) | |
| 70 | |
| 71 if (nargin != 3) | |
| 6046 | 72 print_usage (); |
| 3200 | 73 endif |
| 74 | |
| 75 [rx, cx] = size (X); | |
| 76 [ry, cy] = size (Y); | |
| 77 if (rx != ry) | |
| 78 error ("gls: incorrect matrix dimensions"); | |
| 79 endif | |
| 80 | |
| 81 O = O^(-1/2); | |
| 82 Z = kron (eye (cy), X); | |
| 83 Z = O * Z; | |
| 84 Y1 = O * reshape (Y, ry*cy, 1); | |
| 85 U = Z' * Z; | |
| 86 r = rank (U); | |
| 87 | |
| 88 if (r == cx*cy) | |
| 89 B = inv (U) * Z' * Y1; | |
| 90 else | |
| 91 B = pinv (Z) * Y1; | |
| 92 endif | |
| 93 | |
| 94 BETA = reshape (B, cx, cy); | |
| 95 R = Y - X * BETA; | |
| 96 v = (reshape (R, ry*cy, 1))' * (O^2) * reshape (R, ry*cy, 1) / (rx*cy - r); | |
| 97 | |
| 98 endfunction |