A sufficient statistic and a nonstandard linearization in nonlinear regression

In a nonlinear model y = q(0) + e a standard linearization consists in linearizing n(0) at a point 0*, and in computing the M. L. estimate T(y, 0*) in the linearized model. We propose to take T(Y):= (T(Y,0), ...,T(y,0)) for some 0,...,0 (= the sufficient statistic), linearize each T(y, 0) separately, and then to compute the M. L. estimate 0(y). The variable 0(y) has a smaller variance than T(y, 0), and a comparable bias. Further, 0(y) can be used to approximate the posterior density in a Bayesian approach. The construction of the sufficient statistic has a geometrical background. Possible consequences for nonlinear experimental design are mentioned.