Some facts about functionals of location and scatter

Robust estimation of multivariate location and scatter in the presence of cellwise and casewise contamination

Multivariate location and scatter matrix estimation is a cornerstone in multivariate data analysis. We consider this problem when the data may contain independent cellwise and casewise outliers. Flat data sets with a large number of variables and a relatively small number of cases are common place in modern statistical applications. In these cases global down-weighting of an entire case, as performed by traditional robust procedures, may lead to poor results. We highlight the need for a new generation of robust estimators that can efficiently deal with cellwise outliers and at the same time sh…

α对称分布下的位置和散射半空间中位数

Location and scatter halfspace median under α-symmetric distributions

本文研究了α对称分布下位置和散射半空间中位数的估计性能，提出改进的散射半空间深度以适应更广泛分布，并推导了相关上界。

Differentiability of M-functionals of location and scatter based on t likelihoods

The paper aims at finding widely and smoothly defined nonparametric location and scatter functionals. As a convenient vehicle, maximum likelihood estimation of the location vector m and scatter matrix S of an elliptically symmetric t distribution on d-dimensional space with degrees of freedom larger than 1 extends to an M-functional defined on all probability distributions P in a weakly open, weakly dense domain U. Here U consists of P not putting too much mass in hyperplanes of dimension < d, as shown for empirical measures by Kent and Tyler, Ann. Statist. 1991. It is shown here that (m,S) is…

On Asymptotic Properties of the Separating Hill Estimator

Modeling and understanding multivariate extreme events is challenging, but of great importance in various applications - e.g. in biostatistics, climatology, and finance. The separating Hill estimator can be used in estimating the extreme value index of a heavy tailed multivariate elliptical distribution. We consider the asymptotic behavior of the separating Hill estimator under estimated location and scatter. The asymptotic properties of the separating Hill estimator are known under elliptical distribution with known location and scatter. However, the effect of estimation of the location and s…

Multivariate Location and Scatter Matrix Estimation Under Cellwise and Casewise Contamination

We consider the problem of multivariate location and scatter matrix estimation when the data contain cellwise and casewise outliers. Agostinelli et al. (2015) propose a two-step approach to deal with this problem: first, apply a univariate filter to remove cellwise outliers and second, apply a generalized S-estimator to downweight casewise outliers. We improve this proposal in three main directions. First, we introduce a consistent bivariate filter to be used in combination with the univariate filter in the first step. Second, we propose a new fast subsampling procedure to generate starting po…

Robust and efficient estimation of high dimensional scatter and location

We deal with the equivariant estimation of scatter and location for p-dimensional data, giving emphasis to scatter. It it important that the estimators possess both a high efficiency for normal data and a high resistance to outliers, that is, a low bias under contamination. The most frequently employed estimators are not quite satisfactory in this respect. The Minimum Volume Ellipsoid (MVE) and Minimum Covariance Determinant (MCD) estimators are known to have a very low efficiency. S-Estimators (Davies 1987) with a monotonic weight function like the bisquare behave satisfactorily for "small" p…