A procedure for robust estimation and diagnostics in regression

Abstract

We propose a new procedure for computing an approximation to regression estimates based on the minimization of a robust scale. The procedure can be applied with a large number of independent variables where the usual methods based on resampling require an unfeasible or extremely costly computer time. An important advantage of the procedure is that it can be incorporated in any high breakdown procedure and improve it with just a few seconds of computer time. The procedure minimizes the robust scale over a set of tentative parameter vectors. Each of these parameter vector is obtained as follows. We represent each data point by the vector of changes of the least squares forecasts of that observation, when each of the observations is deleted. Then the sets of possible outliers are obtained as the extreme points of the principal components of these vectors, or as the set of points with large residuals. The good performance of the procedure allows the identification of multiple outliers avoiding masking effects. The efficiency of the procedure for robust estimation and its power as an outlier detection tool are investigated in a simulation study and some examples.