The finite-sample breakdown point of the Oja bivariate median and of the corresponding half-samples version

Abstract

The purpose of this note is twofold. First it is shown that the finite-sample breakdown point of the bivariate median proposed by Oja (1983) is 2/( n + 2) which tends to zero rather than the previously conjectured 1 3 . Then second, it is shown that applying a very general half-samples approach to the Oja criterion function leads to a class of estimators enjoying the 50% breakdown property and containing, as a special case, Rousseeuw's (1985, 1987) minimum covariance determinant estimator.