Minimum volume peeling: A robust nonparametric estimator of the multivariate mode

Among the measures of a distribution’s location, the mode is probably the least often used, although it has some appealing properties. Estimators for the mode of univariate distributions are widely available. However, few contributions can be found for the multivariate case. A consistent direct multivariate mode estimation procedure, called minimum volume peeling, can be outlined as follows. The approach iteratively selects nested subsamples with a decreasing fraction of sample points, looking for the minimum volume subsample at each step. The mode is then estimated by calculating the mean of all points in the final set. The robustness of the method is investigated by analyzing its finite sample breakdown point and algorithms to determine minimum volume sets are discussed. Simulation results confirm that using minimum volume peeling leads to efficient mode estimates both in uncontaminated as well as contaminated situations.