Asymptotic results for inadequate nonlinear models with heteroscedastic variances

Abstract

Several asymptotic results for the nonlinear regression model with heteroscedastic variances are presented. Special attention is paid to so-called inadequate models for both the vector of the unknown expectations as well as for the vector of the unknown variances. It is well known that fitting the data by inadequate models with only few parameters can lead to smaller mean squared errors than fitting by adequate models whereas the latter are known rather seldom only.