Non-linearity measures : a case study

An important problem in applied statistics is fitting a given model function f(fJ) with unknown parameters fJ to a data vector y . Minimizing the residual sum of squares provides the least squares estimates of p. If fUi) is linear in fJ the precision of these estimates is well· known. In a nonlinear case approximate (thauah asymptotically exact) confidence statements can be made. BEALE [I] introduced measures of nonlinea rity which can be used to indicate when approximate confidence statements are appropriate. GUTTMAN and MEETER [2] showed that in some. severely nonlinear. cases Beale's measures do not give the riaht indie-ation. 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).