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Nonlinearity measures: a case study
Author(s) -
Linssen H. N.
Publication year - 1975
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/j.1467-9574.1975.tb00253.x
Subject(s) - mathematics , nonlinear system , residual , non linear least squares , function (biology) , least squares function approximation , statistics , confidence interval , confidence region , explained sum of squares , mathematical optimization , algorithm , physics , quantum mechanics , evolutionary biology , estimator , biology
Summary An important problem in applied statistics is fitting a given model function f (β) with unknown parameters β to a data vector y. Minimizing the residual sum of squares provides the least squares estimates of β. If f (β) is linear in β the precision of these estimates is well‐known. In a nonlinear case approximate (though asymptotically exact) confidence statements can be made. B eale [1] introduced measures of nonlinearity which can be used to indicate when approximate confidence statements are appropriate. G uttman and M eeter [2] showed that in some, severely nonlinear, cases Beale's measures do not give the right indication. In this paper two new nonlinearity measures are introduced and their use is illustrated on a practical problem described by W itt [3]. A more detailed discussion of the theoretical background can be found in references [1] and [2].