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Abstract An iterative procedure for estimating the mode and isopleths of a multivariate distribution is presented. The mode is estimated by selecting a point from the final set in a nested decreasing sequence of convex sets, each one of which is iteratively the smallest closed, convex subset containing a certain proportion of its predecessor's data points. An isopleth is estimated by the boundary of the convex subset corresponding to a fixed number of iterations (independent of n). The method gives rise to a natural density estimator. The estimators are shown to converge almost surely, and convergence rates for the univariate isopleth estimator are presented. Applications to air pollution and health sciences are noted.
Thomas W. Sager (Fri,) studied this question.