Multivariate dispersion orderings

Giovagnoli, Alessandra; Wynn, Henry P.

doi:10.1016/0167-7152(94)00084-l

Cited by 43 publications

(45 citation statements)

References 8 publications

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“…Arnold (1987) proposes R D (F A ) up to a constant and poses the question of which constant makes it bounded by one. Wilks (1960) introduces the volume of a convex body associated with F. Oja (1983) shows that the Wilks index is the expected volume of a simplex generated by d+1 random vertices that are independent and identically distributed according to F ; see also Giovagnoli and Wynn (1995). In our framework, the Wilks index amounts to d+1 times the volume of the lift zonoid (Theorem 5.1).…”

Section: D+1mentioning

confidence: 97%

Multivariate Gini Indices

Koshevoy¹,

Mosler

1997

Journal of Multivariate Analysis

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Two extensions of the univariate Gini index are considered: R D , based on expected distance between two independent vectors from the same distribution with finite mean + # R d ; and R V , related to the expected volume of the simplex formed from d+1 independent such vectors. A new characterization of R D as proportional to a univariate Gini index for a particular linear combination of attributes relates it to the Lorenz zonoid. The Lorenz zonoid was suggested as a multivariate generalization of the Lorenz curve. R V is, up to scaling, the volume of the Lorenz zonoid plus a unit cube of full dimension. When d=1, both R D and R V equal twice the area between the usual Lorenz curve and the line of zero disparity. When d>1, they are different, but inherit properties of the univariate Gini index and are related via the Lorenz zonoid: R D is proportional to the average of the areas of some two-dimensioned projections of the lift zonoid, while R V is the average of the volumes of projections of the Lorenz zonoid over all coordinate subspaces. Academic Press

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Section: D+1mentioning

confidence: 97%

Multivariate Gini Indices

Koshevoy¹,

Mosler

1997

Journal of Multivariate Analysis

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“…Hwang 1985, D-ordering (cf. Giovagnoli and Wynn 1995). Moreover, criteria of type (3) have an obvious relation with peakedness (cf.…”

Section: Definitionmentioning

confidence: 99%

Shape optimal design criterion in linear models

Zaigraev

2002

Metrika

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Abstract. Within the framework of classical linear regression model optimal design criteria of stochastic nature are considered. The particular attention is paid to the shape criterion. Also its limit behaviour is established which generalizes that of the distance stochastic optimality criterion. Examples of the limit maximin criterion are considered and optimal designs for the line fit model are found.

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“…The following Proposition gives conditions under which µ-Bickel-Lehmann implies [11]'s strong dispersion. …”

Section: Relation To Other Multivariate Dispersion Ordersmentioning

confidence: 99%