We investigate the behavior of the nonparametric maximum likelihood estimator f̂n for a decreasing density f near the boundaries of the support of f . We establish the limiting distribution of… (More)

We investigate the limit behavior of the L k-distance between a decreasing density f and its nonparametric maximum likelihood es-timatorˆfn for k ≥ 1. Due to the inconsistency ofˆfn at zero, the case… (More)

An S-estimator of multivariate location and scale minimizes the determinant of the covariance matrix, subject to a constraint on the magnitudes of the corresponding Mahalanobis distances. The… (More)

The MCD estimators of multivariate location and scatter are one of the most popular robust alternatives to the ordinary sample mean and sample covariance matrix. Nowadays they are used to determine… (More)

A large part of the theory of extreme value index estimation is developed for positive extreme value indices. The best known estimator for that case is the Hill estimator. This estimator can be… (More)

In Cator and Lopuhaä [3] an asymptotic expansion for the MCD estimators is established in a very general framework. This expansion requires the existence and non-singularity of the derivative in a… (More)

We give an overview of the different concepts and methods that are commonly used when studying the asymptotic properties of isotonic estimators. After introducing the inverse process, we illustrate… (More)

We provide an asymptotic linear representation for the Breslow estimator for the baseline cumulative hazard function in the Cox model. The representation consists of an average of independent random… (More)

In Cator and Lopuhaä [3] an asymptotic expansion for the MCD estimators is established in a very general framework. This expansion requires the existence and non-singularity of the derivative in a… (More)

The Kaplan-Meier, Nelson-Aalen and Breslow estimators are widely used in the analysis of right-censored time to event data in medical applications. These methods are fully non-parametric and do not… (More)