Nonlinear Stable Least Trimmed Squares for Regression Models with Stable Errors

The common method for estimating nonlinear regression coefficients with Gaussian errors is nonlinear least squares. It is not robust for regression with heavy-tailed errors. The nonlinear least trimmed squares method is an efficient procedure for regression with heavy-tailed errors. We are introducing nonlinear least trimmed squares for the nonlinear regression with non-Gaussian stable errors and estimate the parameters of the stable distributions based on the order statistics. The traditional least trimmed squares regression algorithm is adopted for errors with infinite variance by modifying the trimming procedure. This paper estimated the nonlinear regression coefficients with stable errors through the proposed nonlinear least trimmed squares algorithm based on a new trimming procedure based on the properties of stable order statistics moments. The proposed algorithm was applied to real and simulated datasets and evaluated using a bootstrap standard deviation estimator.