DOI: 10.1017/s0370164600014346. IV.—On Least Squares and Linear Combination of Observations

IV.—On Least Squares and Linear Combination of Observations

10.1017/s0370164600014346

Crossref journal-article

Cambridge University Press (CUP)

Proceedings of the Royal Society of Edinburgh (56)

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 beingu1, 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 thekth.(iii) The sum of squared coefficientswhich measures the mean square error ofyi, is to be a minimum for each value ofi.

Bibliography

Aitken, A. C. (1936). IV.âOn Least Squares and Linear Combination of Observations. Proceedings of the Royal Society of Edinburgh, 55, 42â48.

Authors 1

A. C. Aitken (first)

References 5 Referenced 598

10.1214/aoms/1177732930
{'key': 'S0370164600014346_ref002', 'first-page': '153', 'article-title': '“Notes on Orthogonal Polynomials,”', 'volume': 'lxiv', 'author': 'Lidstone', 'year': '1933', 'journal-title': 'Journ. Inst. Act.'} / Journ. Inst. Act. / “Notes on Orthogonal Polynomials,” by Lidstone (1933)
10.1112/plms/s2-13.1.97
10.1017/S0020268100026652 / Journ. Inst. Act. / “Graduation by Reduction of Mean Square of Error,” by Sheppard (1914)
{'key': 'S0370164600014346_ref003', 'first-page': '348', 'article-title': '“Reduction of Errors by Negligible Differences,”', 'volume': 'ii', 'author': 'Sheppard', 'year': '1912', 'journal-title': 'Proc. Fifth Internat. Congr. Math.'} / Proc. Fifth Internat. Congr. Math. / “Reduction of Errors by Negligible Differences,” by Sheppard (1912)

Dates

Type	When
Created	10 years ago (Aug. 6, 2015, 3:52 a.m.)
Deposited	6 years ago (Aug. 28, 2019, 11:21 p.m.)
Indexed	2 days, 8 hours ago (Sept. 3, 2025, 6:19 a.m.)
Issued	89 years, 8 months ago (Jan. 1, 1936)
Published	89 years, 8 months ago (Jan. 1, 1936)
Published Online	10 years, 11 months ago (Sept. 15, 2014)
Published Print	89 years, 8 months ago (Jan. 1, 1936)

Funders 0

None

BibTeX

@article{Aitken_1936, title={IV.—On Least Squares and Linear Combination of Observations}, volume={55}, ISSN={0370-1646}, url={http://dx.doi.org/10.1017/s0370164600014346}, DOI={10.1017/s0370164600014346}, journal={Proceedings of the Royal Society of Edinburgh}, publisher={Cambridge University Press (CUP)}, author={Aitken, A. C.}, year={1936}, pages={42–48} }

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