Note on the spatial quantile of a random vector

B. Abdous and R. Theodorescu

Statistics & Probability Letters, 1992, vol. 13, issue 4, 333-336

Abstract: Let [alpha] [set membership, variant] (0, 1); the [alpha]-quantile of an -valued (k [greater-or-equal, slanted] 1) random variable X is a point minimizing the expectation E(||X - [theta]||p,[alpha] - ||X||p,[alpha]), where ||·||p,[alpha] is defined in terms of the lp-norm, 1 [less-than-or-equals, slant] p [less-than-or-equals, slant] [infinity], and [alpha] [set membership, variant] (0, 1). The properties of such an [alpha]-quantile extend those obtained previously for [alpha] = 0.5, i.e. for the median (see Kemperman, 1987). Computational aspects are also discussed.

Keywords: Spatial; quantile; spatial; median; convexity (search for similar items in EconPapers)
Date: 1992
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Citations: View citations in EconPapers (19)

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