Linear least squares
In order that Bienaymé’s papers on this subject appear in their proper perspective, we shall give a brief history of the earlier probabilistic aspects of linear least squares, particularly as developed by Gauss and Laplace, in the next section. Both these authors are frequently mentioned in Bienaymé’s contributions, which are, naturally, strongly motivated and colored by the work of Laplace. The work of Gauss in this area is well described by Plackett (1949) and Seal (1967). Before proceeding, a few remarks at this stage about the general nature of the motivating problem will help elucidate the whole development of this chapter. We shall use modern matrix notation in our exposition and shall otherwise simplify the original mathematical notation where convenient. It is well to note, however, that use of modern notation obscures many of the difficulties encountered by the original workers.
KeywordsInterpolation Theory Cauchy Functional Equation Probabilistic Side Compte Rendu Interpolational Part
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