Robustifying the Least Squares estimate of parameters of variance model function in nonlinear regression with heteroscedastic variance

The purpose of this research is to propose a robust estimate for the parameters of a nonlinear regression model and its residual variance model parameters, when the residuals follow a heteroscedastic parametric model function. The classic estimate is based on the least squares estimation error for the model parameters and the least square estimate error between sample variance and variance model, for the parameters of variance function model. The sample variance that are computed from the data set, are used as the initial estimates of variance model. In the presence of outliers these estimators are not Robust, and tends to infinity. Both function model parameter estimates and variance model parameter estimates must be robustified to solve the outlier effect problems. In this research the MM-estimator is applied for robust estimating the function model parameters and M-estimator is applied for robust estimating of variance function model parameters. These estimators finally combined and the Extended Generalized Estimator is calculated.