Nonlinearity measures: a case study

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Abstract
SummaryAn important problem in applied statistics is fitting a given model functionf(β) with unknown parameters β to a data vectory.Minimizing the residual sum of squares provides the least squares estimates of β. Iff(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. Beale[1] introduced measures of nonlinearity which can be used to indicate when approximate confidence statements are appropriate. Guttmanand Meeter[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 Witt[3]. A more detailed discussion of the theoretical background can be found in references [1] and [2].

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