August 2023 Note on Legendre’s Method of Least Squares
Jukka Nyblom
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Statist. Sci. 38(3): 510-513 (August 2023). DOI: 10.1214/23-STS887

Abstract

In the first published treatment of the least squares, Legendre applied his new method to the French meridian data measured for the determination of the length of the meter (Nouvelles méthodes pour la détermination des orbites des comètes (1805) 76 Firmin Didot). Legendre treated one error term as a constant. It is shown here that it turns out to be equivalent to the generalized least squares solution of his model (Nouvelles méthodes pour la détermination des orbites des comètes (1805) 77 Firmin Didot).

Acknowledgments

The author thanks Harri Högmander and Tiia-Maria Pasanen for their help in finalizing the paper. The author also thanks an associated editor and a referee for their constructive criticism and comments.

Citation

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Jukka Nyblom. "Note on Legendre’s Method of Least Squares." Statist. Sci. 38 (3) 510 - 513, August 2023. https://doi.org/10.1214/23-STS887

Information

Published: August 2023
First available in Project Euclid: 20 August 2023

MathSciNet: MR4630958
Digital Object Identifier: 10.1214/23-STS887

Keywords: determination of meter , flattening of the Earth , French meridian data , generalized least squares , meridian arc length

Rights: Copyright © 2023 Institute of Mathematical Statistics

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Vol.38 • No. 3 • August 2023
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