ABSTRACT
A problem that crops up time after time in statistics is that of finding those values of b 0 , b 1 bm that cause a criterion function https://www.w3.org/1998/Math/MathML"> C = b 0 + a 1 b 1 + a 2 b 2 + ⋯ + a m b m + c 1 b 1 2 + c 2 b 2 2 + ⋯ + c m b m 2 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781410600455/7454c2b5-d6ca-4a0d-9c7c-eb119d80c318/content/eqn1_677_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> to take on its largest (or smallest) possible value. The bs here are unknowns, while the as and the cs are known constants (usually sums or sums of squares of data values). This is a problem for which the tools of differential calculus are ideally suited. We shall of course barely tap the wealth of techniques available in that branch of mathematics.
