Our aim is to construct a factor analysis method that can resist the effect of outliers. For this we start with a highly robust initial covariance estimator, after which the factors can be obtained from maximum likelihood or from principal factor analysis (PFA). We find that PFA based on the...

It is well-known that k-step M-estimators can yield a high efficiency without losing the breakdown point of the initial estimator. In this note we derive their bias curves. In the location framework the bias increases only slightly with k, but in the scale case the bias curves change considerably.

Deepest regression (DR) is a method for linear regression introduced by P. J. Rousseeuw and M. Hubert (1999, J. Amer. Statis. Assoc.94, 388-402). The DR method is defined as the fit with largest regression depth relative to the data. In this paper we show that DR is a robust method, with...

In this paper we investigate the robustness properties of the deepest regression, a method for linear regression introduced by Rousseeuw and Hubert [6]. We show that the deepest regression functional is Fisher-consistent for the conditional median, and has a breakdown value of in all dimensions....

In this paper we introduce the least-trimmed squares estimator for multivariate regression. We give three equivalent formulations of the estimator and obtain its breakdown point. A fast algorithm for its computation is proposed. We prove Fisher-consistency at the multivariate regression model...