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...

In this note we study the problem of estimating the parameters of the conditional median function at elliptical models. For this we use positive-breakdown estimators of multivariate location and scatter, and obtain influence functions and asymptotic variances of the resulting slope and...

For multivariate data, the halfspace depth function can be seen as a natural and affine equivariant generalization of the univariate empirical cdf. For any multivariate data set, we show that the resulting halfspace depth function completely determines the empirical distribution. We do this by...

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.

This paper reviews some aspects of positive-breakdown regression that have been discussed. Apart from efficiency, also some related topics are addressed in order to obtain a broader view. Several unusual aspects are shown to be intimately connected with the exact fit property. It is argued that...

For the computation of high-breakdown (HB) regression one typically uses an algorithm based on randomly selected p-subsets, where p is the number of parameters. This resampling algorithm may itself break down, with a probability that decreases with the number of p-subsets generated. In order to...