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 u 1 , u 2 , …, u n , 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 y i , is to be a minimum for each value of i .
Keywords
MathematicsEquidistantUncorrelatedRepresentation (politics)Least-squares function approximationSquare (algebra)Series (stratigraphy)Value (mathematics)Set (abstract data type)Degree (music)CombinatoricsMean valuePolynomialMean squared errorStatisticsMathematical analysisGeometryComputer sciencePhysics
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Publication Info
- Year
- 1936
- Type
- article
- Volume
- 55
- Pages
- 42-48
- Citations
- 875
- Access
- Closed
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Cite This
A. C. Aitken
(1936).
IV.—On Least Squares and Linear Combination of Observations.
Proceedings of the Royal Society of Edinburgh
, 55
, 42-48.
https://doi.org/10.1017/s0370164600014346
Identifiers
- DOI
- 10.1017/s0370164600014346