On influence assessment for LAD regression

Abstract

Least absolute deviations (LAD) regression, i.e. L 1 regression, is more resistant to the outliers in the response variable than the least-squares regression, but is relatively sensitive to outlying observations in explanatory variables. However, some but few attentions have been contributed to the influence assessment for LAD regression, especially for LAD nonlinear regression. In this paper, we propose several diagnostic measures, which can be used for LAD regression models. The quasi-likelihood distance based on the L 1 objective function, Cook distance based on the elliptical norm and some other diagnostic measures are introduced for LAD regression, and two examples are given to illustrate the use of these measures. The diagnostic models for LAD regression are also investigated. It is proved that the estimators of the case deletion model (CDM) and the mean shift outlier model (MSOM) are equal in linear and nonlinear LAD regression models.