Amirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-2449Articles in Press20240505The competition of robust methods in linear and nonlinear regression with heavy-tailed stable errors540410.22060/ajmc.2024.22960.1207ENMohammadBassam Shiekh AlbasatnehDepartment of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), IranOmidNaghshineh ArjmandDepartment of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Iran0000-0002-7435-2733Journal Article20240203Robust regression methods including Least Trimmed Squares are one of the most important methodologies to compute exact coeﬃcient estimators when data is polluted with outliers. There is interest to generalize Least Trimmed Squares for regression models with heavy-tailed stable errors. In this manuscript, we compare estimating coeﬃcients methods with the robust Least Trimmed Squares method in stable errors case. Therefore, we propose Stable Least Trimmed Squares and Nonlinear Stable Least Trimmed Squares methods for linear/nonlinear regression models with stable errors, respectively. The joint distribution of ordered errors is used with the ﬁnite variance property of ordered stable errors, whose indexes are deﬁned by cut-oﬀ points. We make many comparisons using simulated and real datasets.