IV.—On Least Squares and Linear Combination of Observations
- 1 January 1936
- journal article
- conference paper
- Published by Cambridge University Press (CUP) in Proceedings of the Royal Society of Edinburgh
- Vol. 55, 42-48
- https://doi.org/10.1017/s0370164600014346
Abstract
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 kth. (iii) The sum of squared coefficients which measures the mean square error of yi , is to be a minimum for each value of i.Keywords
This publication has 3 references indexed in Scilit:
- A Postulate for ObservationsThe Annals of Mathematical Statistics, 1932
- Graduation by Reduction of Mean Square of ErrorJournal of the Institute of Actuaries, 1914
- Fitting of Polynomial by Method of Least Squares (Solution in Terms of Differences or Sums)Proceedings of the London Mathematical Society, 1914