Gauss' method of least squares: an historically-based introduction

Identifier

etd-0707103-145026

Author

Belinda B. Brand, Louisiana State University and Agricultural and Mechanical CollegeFollow

Degree

Master of Science (MS)

Department

Mathematics

Document Type

Thesis

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.

Date

2003

Document Availability at the Time of Submission

Release the entire work immediately for access worldwide.

Recommended Citation

Brand, Belinda B., "Gauss' method of least squares: an historically-based introduction" (2003). LSU Master's Theses. 2097.
https://repository.lsu.edu/gradschool_theses/2097

Committee Chair

James J. Madden

DOI

10.31390/gradschool_theses.2097