Leverage and Breakdown in L 1 Regression
Year: 1992
Type: article
Abstract: In this article the notion of leverage of a design point when fitting a linear regression model is interpreted geometrically. In the case of least squares fitting, the leverage indicators based on the diagonal of the hat matrix are widely applied. By interpreting these hat matrix indicators geometrically, leverage can be generalized to groups of design points, as well as to other methods of fitting. The article introduces a leverage indicator that is appropriate for L 1 regression and discusses some aspects of this new diagnostic. It is shown that, in the case of L 1 regression, the leverage indicators have a precise interpretation. They tell us about the breakdown and/or the exactness of fit. As an application, the article considers the maximal possible breakdown value of L 1 regression and the choice of designs that achieve this maximum.
Authors: Steven P. Ellis, Stephan Morgenthaler
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1977735854