NAME
Statistics::GaussHelmert - General weighted least squares estimation
DESCRIPTION
This module is a flexible tool for estimating model parameters given a
set of observations. The module provides function for a linear
estimation model, the underlying model is called Gauss-Helmert model.
Statistics::GaussHelmert is different to modules such as Statistics::OLS
in the sense that it may fit arbitrary functions to data of any
dimensions. You have to specify an implicit minimization function (in
contrast to explicit functions as in traditional regression methods) and
its derivatives with respects to the unknown and the observations. You
may also specify constraint function on the unknowns (with its
derivative). Furthermore you already need an approximate solution. For
some problems it is easy finding approximate solutions by directly
solving for the unknown parameters with some well chosen observations.
REQUIREMENTS
This module requires Perl 5.6.0 and PDL 2.3.2. Furthermore it
requires Math::Random for testing purposes. Note that installing
PDL requires a series of other modules such as ExtUtils::F77, etc.
LITERATURE
Press et al. (1992) Numerical Recipes in C, 2nd Ed., Cambridge
University Press, Chapter 15.
Chapter 15, "Modeling of Data", deals with general weighted least
squares estimation, though it describes the Levenber-Marquardt
method in more detail. Additionally, it is assumed that only one
maesurement is observed.
Mikhail, E.M. and Ackermann, F. (1976): Observations and Least Squares
University Press of America
This book covers the classical Gauss-Helmert model.
Koch, K. (1999) Parameter Estimation and Hypothesis Testing in Linear
Models, Springer Verlag, 2nd edition
This book covers the Gauss-Markoff model, a cousin of the
Gauss-Helmert model, but modelling explicit functions.
AUTHOR
Stephan Heuel (perl@heuel.org)
COPYRIGHT
Copyright (C) 2000/2001 Stephan Heuel and Institute for Photogrammetry,
University of Bonn. All rights reserved. There is no warranty. You are
allowed to redistribute this software / documentation under certain
conditions, see the GNU Public License, GPL for details,
http://www.gnu.org/copyleft/gpl.html.