Leveraged least trimmed absolute deviations

Abstract The design of regression models that are not affected by outliers is an important task which has been subject numerous papers within the statistics community for last decades. Prominent examples robust least trimmed squares (LTS), where k largest squared deviations ignored, and absolute (LTA) ignores deviations. numerical complexity both driven number binary variables value ignored We introduce leveraged (LLTA) exploits LTA already immune against y -outliers. Therefore, LLTA only to be guarded outlying values in x , so-called leverage points, can computed beforehand, contrast Thus, while mixed-integer formulations LTS have as many data needs one variable per point, resulting a significant reduction variables. Based on 11 sets from literature, we demonstrate (1) LLTA’s prediction quality improves much faster than fast increasing (2) solves benchmark problems about 80 times five LTA, median.