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
Affiliated Institutions
Related Publications
Least Median of Squares Regression
Abstract Classical least squares regression consists of minimizing the sum of the squared residuals. Many authors have produced more robust versions of this estimator by replaci...
The coefficient of determination R-squared is more informative than SMAPE, MAE, MAPE, MSE and RMSE in regression analysis evaluation
Regression analysis makes up a large part of supervised machine learning, and consists of the prediction of a continuous independent target from a set of other predictor variabl...
ROBUST MODELING WITH ERRATIC DATA
An attractive alternative to least‐squares data modeling techniques is the use of absolute value error criteria. Unlike the least‐squares techniques the inclusion of some infini...
A Linear Spatial Correlation Model, with Applications to Positron Emission Tomography
Abstract A simple spatial-correlation model is presented for repeated measures data. Correlation between observations on the same subject is assumed to decay as a linear functio...
Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation
Traditional econometric models assume a constant one-period forecast variance. To generalize this implausible assumption, a new class of stochastic processes called autoregressi...
Publication Info
- Year
- 1936
- Type
- article
- Volume
- 55
- Pages
- 42-48
- Citations
- 875
- Access
- Closed
External Links
Social Impact
Altmetric
PlumX Metrics
Social media, news, blog, policy document mentions
Citation Metrics
875
OpenAlex
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