Abstract
Asymmetric multivariate probability distributions can be difficult to characterize in terms of their location. The works of Doksum (1975, Scand. J. Statist., 2, 11–22) and Blough (1985, Ann. Inst. Statist. Math., 37, 545–555) provide the construction of a location region for a given distribution. Any point in this closed, convex region will serve as a location parameter. It is the purpose of this paper to obtain a consistent estimator of the location region. Consistency is defined in terms of an appropriate pseudometric.
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References
Birkhoff, G. and MacLane, S. (1971). A Survey of Modern Algebra, 3rd ed., MacMillan, New York.
Blough, David K. (1985). Measures of location in the plane, Ann. Inst. Statist. Math., 37, 545–555.
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Doksum, K. A. (1975). Measures of location and asymmetry, Scand. J. Statist., 2, 11–22.
Oja, H. (1983). Descriptive statistics for multivariate distributions, Statist. Probab. Lett., 6, 327–332.
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Blough, D.K. Consistent estimation of location region. Ann Inst Stat Math 40, 343–352 (1988). https://doi.org/10.1007/BF00052349
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DOI: https://doi.org/10.1007/BF00052349