Nonlinearity measures: a case study

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].