6533b832fe1ef96bd129a433

RESEARCH PRODUCT

The simplex dispersion ordering and its application to the evaluation of human corneal endothelia

Miguel Lopez-diazGuillermo AyalaSmabss Rg

subject

CombinatoricsConvex hullStatistics and ProbabilityNumerical AnalysisHausdorff distanceSimplexMultivariate random variableHausdorff spaceRegular polygonUnivariateStatistical dispersionStatistics Probability and UncertaintyMathematics

description

A multivariate dispersion ordering based on random simplices is proposed in this paper. Given a R^d-valued random vector, we consider two random simplices determined by the convex hulls of two independent random samples of sizes d+1 of the vector. By means of the stochastic comparison of the Hausdorff distances between such simplices, a multivariate dispersion ordering is introduced. Main properties of the new ordering are studied. Relationships with other dispersion orderings are considered, placing emphasis on the univariate version. Some statistical tests for the new order are proposed. An application of such ordering to the clinical evaluation of human corneal endothelia is provided. Different analyses are included using an image database of human corneal endothelia.

yearjournalcountryeditionlanguage
2009-08-01Journal of Multivariate Analysis
10.1016/j.jmva.2008.12.017http://dx.doi.org/10.1016/j.jmva.2008.12.017