Type of Document	Master's Thesis
Author	Brand, Belinda B.
Author's Email Address	bbrand@lsu.edu
URN	etd-0707103-145026
Title	Gauss' Method of Least Squares: An Historically-Based Introduction
Degree	Master of Science (M.S.)
Department	Mathematics
Advisory Committee	Advisor Name Title James J. Madden Committee Chair Frank Neubrander Committee Member Padmanabham Sundar Committee Member
Keywords	probability theory mathematical statistics statistics
Date of Defense	2003-07-03
Availability	unrestricted
Abstract This work presents Gauss' justification of the method of least squares, following the treatment given by Gauss himself in "Theoria Combinationis Observationum Erroribus Minimis Obnoxiae," where the main idea is to show that the least squares estimate is the unbiased linear estimate of minimum variance. (Actually, we present Gauss' argument both in his terminology and translated into matrix terminology.) We show how this contrasts with Gauss' earlier justfication in "Theoria Motus Corporum Coelestium" which was based on the assumption of a normal distribution of errors, and yielded the estimate of maximum likelihood. We present as a background the development from scratch of all the probability theory needed, albeit we have not treated explicitly all the needed measure theory.
Files	Filename       Size       Approximate Download Time (Hours:Minutes:Seconds)     28.8 Modem   56K Modem   ISDN (64 Kb)   ISDN (128 Kb)   Higher-speed Access    Brand_thesis.pdf 322.03 Kb 00:01:29 00:00:46 00:00:40 00:00:20 00:00:01