New robust dynamic plots for regression mixture detection

The forward search is a powerful general method for detecting multiple masked outliers and for determining their effect on inferences about models fitted to data. From the monitoring of a series of statistics based on subsets of data of increasing size we obtain multiple views of any hidden structure. One of the problems of the forward search has always been the lack of an automatic link among the great variety of plots which are monitored. Usually it happens that a lot of interesting features emerge unexpectedly during the progression of the forward search only when a specific combination of forward plots is inspected at the same time. Thus, the analyst should be able to interact with the plots and redefine or refine the links among them. In the absence of dynamic linking and interaction tools, the analyst risks to miss relevant hidden information. In this paper we fill this gap and provide the user with a set of new robust graphical tools whose power will be demonstrated on several regression problems. Through the analysis of real and simulated data we give a series of examples where dynamic interaction with different “robust plots” is used to highlight the D. Perrotta Global Security and Crisis Management Unit, Institute for the Protection and Security of the Citizens, Joint Research Centre, European Commission, 21027 Ispra, Italy e-mail: [email protected] M. Riani (B) Dipartimento di Economia, Division of Statistics and Computing, Università di Parma, Via Kennedy 6, 43100 Parma, Italy e-mail: [email protected] F. Torti Dipartimento di Statistica, Università di Milano Bicocca, Via Arcimboldi 8, 20126 Milan, Italy e-mail: [email protected] F. Torti Dipartimento di Economia, Università di Parma, Via Kennedy 6, 43100 Parma, Italy