A strong i.i.d. representation is obtained for the product-limit estimator of the survival function based on left truncated and right censored data. This extends the result of Chao and Lo (1988, Ann. Statist.16, 661-668) for truncated data. An improved rate of the approximation is also obtained...

A robust correlation estimator based on the spatial sign covariance matrix (SSCM) is proposed. We derive its asymptotic distribution and influence function at elliptical distributions. Finite sample and robustness properties are studied and compared to other robust correlation estimators by...

We derive the asymptotical distributions of two-sample U-statistics and two-sample empirical U-quantiles in the case of weakly dependent data. Our results apply to observations that can be represented as functionals of absolutely regular processes, including e.g. many classical time series...

An S-estimator of regression is obtained by minimizing an M-estimator of scale applied to the residuals ri. On the other hand, a generalized S-estimator (or GS-estimator) minimizes an M-estimator of scale based on all pairwise differences ri - rj. Generalized S-estimators have similar robustness...

In this paper we introduce generalized S-estimators for the multivariate regression model. This class of estimators combines high robustness and high efficiency. They are defined by minimizing the determinant of a robust estimator of the scatter matrix of differences of residuals. In the special...

In this paper, the influence functions and limiting distributions of the canonical correlations and coefficients based on affine equivariant scatter matrices are developed for elliptically symmetric distributions. General formulas for limiting variances and covariances of the canonical...

In this paper it is studied how observations in the training sample affect the misclassification probability of a quadratic discriminant rule. An approach based on partial influence functions is followed. It allows to quantify the effect of observations in the training sample on the performance...

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...

The minimum covariance determinant (MCD) scatter estimator is a highly robust estimator for the dispersion matrix of a multivariate, elliptically symmetric distribution. It is relatively fast to compute and intuitively appealing. In this note we derive its influence function and compute the...

Li and Chen (J. Amer. Statist. Assoc. 80 (1985) 759) proposed a method for principal components using projection-pursuit techniques. In classical principal components one searches for directions with maximal variance, and their approach consists of replacing this variance by a robust scale...