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.
Publisher
Cambridge University Press (CUP)
Subject
General Medicine,General Chemistry
Reference5 articles.
1. A Postulate for Observations
2. “Notes on Orthogonal Polynomials,”;Lidstone;Journ. Inst. Act.,1933
3. Fitting of Polynomial by Method of Least Squares (Solution in Terms of Differences or Sums)
4. “Graduation by Reduction of Mean Square of Error,”;Sheppard;Journ. Inst. Act.,1914
5. “Reduction of Errors by Negligible Differences,”;Sheppard;Proc. Fifth Internat. Congr. Math.,1912
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