IV.—On Least Squares and Linear Combination of Observations | Proceedings of the Royal Society of Edinburgh | Cambridge Core (original) (raw)

Extract

In a series of papers W. F. Sheppard (1912, 1914) has considered the approximate representation of equidistant, equally weighted, and uncorrelated observations under the following assumptions:–

(i) The data being u1, u2, …, un , the representation is to be given by linear combinations

(ii) The linear combinations are to be such as would reproduce any set of values that were already values of a polynomial of degree not higher than the _k_th.

(iii) The sum of squared coefficients which measures the mean square error of yi , is to be a minimum for each value of i.

References

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Sheppard, W. F., 1912. “Reduction of Errors by Negligible Differences,” Proc. Fifth Internat. Congr. Math. (Cambridge), vol. ii, pp. 348–384.Google Scholar

Sheppard, W. F., 1914. “Fitting of Polynomials by Method of Least Squares,” Proc. Lond. Math. Soc. (2), vol. xiii, pp. 97–108.CrossRefGoogle Scholar

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