This article studies the outlier detection problem from the standpoint of penalized regression. In the regression model, we add one mean shift parameter for each of the n data points.

Dehan Kong, Howard D. Bondell, Yichao Wu, FULLY EFFICIENT ROBUST ESTIMATION, OUTLIER DETECTION AND VARIABLE SELECTION VIA PENALIZED REGRESSION, Statistica Sinica, Vol. 28, No. 2, Computer Experiments ...

The method adopts multiple regression methods, and the regression residuals are used to discriminate outliers.