Robust trimmed regression for heavy-tailed stable data: Competing methods and order statistics

Robust regression methods including, least trimmed squares, are among the most important methodologies for computing exact coefficient estimators when data is polluted with outliers. There is interest in generalizing least trimmed squares for regression models with heavy-tailed stable errors. This manuscript, compares 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 (Subsection 3.1). We make many comparisons using simulated and real datasets.