Statistical Foundations of the Method of Least Squares

Abstract

In Chapter 8, we will discuss Gauss’s 1809 derivation of the method of least squares. In order to trace the intellectual origins of this method, we must return to 1772. In that year, Jean Bernoulli III published a review of the 1770 French translation of Maire and Boscovich’s geodetic survey. Attached to this review is a footnote which may be translated as follows:

“The problem of finding the true mean of a certain number of observations (which is rarely the arithmetic mean), is of great interest to astronomers; it is to be hoped that someone will present the closely related essence of the different methods given for this purpose by Fr Boscovich, by Mr Lambert [1770] in the work cited on page 157 of my first volume, by Mr Daniel Bernoulli in a short memoir which has not yet been published, and finally by Mr de la Grange in a beautiful treatise which he has recently made the subject of several lectures at our academic meetings.” [Author’s translation from Stigler’s (1978b) transcription]