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Medientyp:
E-Artikel
Titel:
Quantile functions for multivariate analysis: approaches and applications
Beteiligte:
Serfling, Robert
Erschienen:
Wiley, 2002
Erschienen in:
Statistica Neerlandica, 56 (2002) 2, Seite 214-232
Sprache:
Englisch
DOI:
10.1111/1467-9574.00195
ISSN:
1467-9574;
0039-0402
Entstehung:
Anmerkungen:
Beschreibung:
Despite the absence of a natural ordering of Euclidean space for dimensions greater than one, the effort to define vector‐valued quantile functions for multivariate distributions has generated several approaches. To support greater discrimination in comparing, selecting and using such functions, we introduce relevant criteria, including a notion of “medianoriented quantile function”. On this basis we compare recent quantile approaches and several multivariate versions of trimmed mean and interquartile range. We also discuss a univariate “generalized quantile” approach that enables particular features of multivariate distributions, for example scale and kurtosis, to be studied by two‐dimensional plots. Methods based on statistical depth functions are found to be especially attractive for quantile‐based multivariate inference.