In this paper we introduce weighted estimators of the location and dispersion of a multivariate data set with weights based on the ranks of the Mahalanobis distances. We discuss some properties of the estimators like the breakdown point, influence function and asymptotic variance. The outlier detection capacities of different weight functions are compared. A simulation study is given to investi...

Rousseeuw’s minimum covariance determinant (MCD) method is a highly robust estimator of multivariate mean and covariance. In practice, the MCD covariance estimator may be singular. However, a nonsingular covariance estimator is required to calculate the Mahalanobis distance. In order to fix this singular problem, we propose an improved version of the MCD estimator, which is a combination of the...

The purpose of this paper is to identify the effective points on the performance of one of the important algorithm of data mining namely support vector machine. The final classification decision has been made based on the small portion of data called support vectors. So, existence of the atypical observations in the aforementioned points, will result in deviation from the correct decision. Thus...

In this paper, we propose a new componentwise estimator of a dispersion matrix, based on a highly robust estimator of scale. The key idea is the elimination of a location estimator in the dispersion estimation procedure. The robustness properties are studied by means of the influence function and the breakdown point. Further characteristics such as asymptotic variance and efficiency are also an...

The minimum covariance determinant (MCD) method of Rousseeuw (1984) is a highly robust estimator of multivariate location and scatter. Its objective is to nd h observations (out of n) whose covariance matrix has the lowest determinant. Until now applications of the MCD were hampered by the computation time of existing algorithms, which were limited to a few hundred objects in a few dimensions. ...

The Minimum Covariance Determinant (MCD) estimator is a highly robust procedure for estimating the centre and shape of a high dimensional data set. It consists of determining a subsample of h points out of nwhichminimises the generalised variance. By definition, the computation of this estimator gives rise to a combinatorial optimisation problem, forwhich several approximate algorithms have bee...