Note on the spatial quantile of a random vector

Let α ∈ (0, 1); the α-quantile of an R k -valued ( k ⩾ 1) random variable X is a point θ ∈ R k minimizing the expectation E(‖ X − θ‖ p , α − ‖ X‖ p , α ), where ‖·‖ p , α is defined in terms of the ℓ p -norm, 1 ⩽ p ⩽ ∞, and α ∈ (0, 1). The properties of such an α-quantile extend those obtained previ...

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Bibliographic Details
Published in:Statistics & probability letters 1992-03, Vol.13 (4), p.333-336
Main Authors: Abdous, B., Theodorescu, R.
Format: Article
Language:English
Subjects:
convexity
Distribution theory
Exact sciences and technology
Mathematics
Probability and statistics
Sciences and techniques of general use
spatial median
Spatial quantile
Spatial quantile spatial median convexity
Statistics
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Summary:Let α ∈ (0, 1); the α-quantile of an R k -valued ( k ⩾ 1) random variable X is a point θ ∈ R k minimizing the expectation E(‖ X − θ‖ p , α − ‖ X‖ p , α ), where ‖·‖ p , α is defined in terms of the ℓ p -norm, 1 ⩽ p ⩽ ∞, and α ∈ (0, 1). The properties of such an α-quantile extend those obtained previously for α = 0.5, i.e. for the median (see Kemperman, 1987). Computational aspects are also discussed.
ISSN:0167-7152
1879-2103
DOI:10.1016/0167-7152(92)90043-5