Abstract
ABSTRACTTo estimate the central tendency or location of a sample of interval-valued data, a standard statistic is the interval-valued sample mean. Its strong sensitivity to outliers or data changes motivates the search for more robust alternatives. In this respect, a more robust location statistic is studied in this paper. This measure is inspired by the concept of spatial median and makes use of the versatile generalized Bertoluzza's metric between intervals, the so-called distance. The problem of minimizing the mean distance to the values the random interval takes, which defines the spatial-type -median, is analysed. Existence and uniqueness of the sample version are shown. Furthermore, the robustness of this proposal is investigated by deriving its finite sample breakdown point. Finally, a real-life example from the Economics field illustrates the robustness of the sample-median, and simulation studies show some comparisons with respect to the mean and several recently introduced robust location measures for interval-valued data.
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