On Beale's Measures of Non-linearity

On Beale's Measures of Non-linearity

Measures of non-linearity that have been developed by Beale (1960a), are designed to indicate when the degree of non-linearity in a non-linear estimation problem is small enough to justify using the usual linear model theory results as approximations. The validity and usefulness of the measures is e...

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Veröffentlicht in:Technometrics 1965-11, Vol.7 (4), p.623-637
Hauptverfasser: Guttman, Irwin, Meeter, Duane A.
Format: Artikel
Sprache:eng
Schlagworte:
Approximation
Ellipses
Least squares
Linear approximation
Linear transformations
Mathematical vectors
Mean square values
Parametric models
Quadratic approximation
Tangent planes
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Zusammenfassung:Measures of non-linearity that have been developed by Beale (1960a), are designed to indicate when the degree of non-linearity in a non-linear estimation problem is small enough to justify using the usual linear model theory results as approximations. The validity and usefulness of the measures is examined by means of numerical examples. Explanations for the behaviour of the measures is offered and the results are discussed.
ISSN:0040-1706
1537-2723
DOI:10.1080/00401706.1965.10490303