1 Oscar Sheynin History of Statistics Berlin, 2012 ISBN 978-3 ...

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1 Oscar Sheynin History of Statistics Berlin, 2012 ISBN 978-3 ...

[aa] ˆx + [ab] ŷ + … + [as] = 0, [ab] ˆx + [bb] ŷ + … + [bs] = 0, …,(5)having a positive definite and symmetric matrix. For direct measurementsthe same condition (3) leads to the arithmetic mean. Gauss (1828) devisedanother no less important and barely known to statisticians pattern ofadjusting indirect observations.9.1.2. The Priority Strife. Legendre (1805, pp. 72 – 73) was the first tostate publicly the condition of least squares. Declaring that the extremeerrors without regard to sign should be contained within as narrow limits aspossible (which is achieved by the minimax principle rather than by leastsquares!), he, as translated by Hald (1998, p. 119), continued:Among all the principles [of adjusting observations] I think there is noone more general, more exact and more easy to apply than that which wehave made use of in the preceding researches [in the same contribution],and which consists in making the sum of the squares of the errors aminimum. In this way there is established a sort of equilibrium among theerrors, which prevents the extremes to prevail and is well suited to make usknow the state of the system most near the truth.Here, Legendre made a mistake: he should have mentioned not errors, butresiduals. Those shortcomings did not deter Stigler (1986, p. 13) who calledLegendre’s exposition One of the clearest and the most elegant introductionof a new statistical method in the history of statistics. And on p. 146 Stiglerwrongly praised Legendre as opposed to Gauss.Gauss publicly derived the principle of least squares in 1809, but stated(1809, § 186) that he had applied the condition of least squares from 1794 or1795 and called it his own. His statement offended Legendre (letter to Gaussof 31 May 1809, see Gauss, W-9, p. 309) as well as other Frenchmathematicians although not Laplace.Gauss (letter of 17.10.1824 to H. C. Schumacher), see W/Erg-5, Tl. 1, p.413) bitterly lamented over Legendre’s fate:With indignation and distress I have […] read that the pension of theelderly Legendre, an ornament to his country and his epoch, was cancelled.May (1972, p. 309) formulated a likely opinion about the problem ofpriority as approached by Gauss:Gauss cared a great deal for priority. […] But to him this meant beingfirst to discover, not first to publish; and he was satisfied to establish hisdates by private records, correspondence, cryptic remarks in publications.[…] Whether he intended it so or not, in this way he maintained theadvantage of secrecy without losing his priority in the eyes of latergenerations.Here is another comment (Biermann 1966, p. 18): What is forbidden forusual authors, ought to be allowed for Gausses and in any case we mustrespect his [Gauss’] initial considerations.81

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