A new stochastic estimator for symmetry center in multidimensional space

Abstract

We consider a new robust stochastic algorithm for estimating the symmetry center of multivariate distributions with convex centrally symmetric density level surfaces. We investigate its time complexity, convergence rate, and robustness. A modification of the algorithm that improves estimation accuracy is also discussed. Comparative numerical experiments with existing multivariate location parameter estimation algorithms, including Tukey, Oja, and geometric medians, are presented. Since in the considered class of distributions these algorithms estimate the symmetry center, the comparison is objective