Nonparametric notions of multivariate scatter measure and more scattered based on statistical depth functions

[摘要] Nonparametric notions of multivariate scatter measure and more scattered, based on statistical depth functions, are investigated. In particular, notions of more scattered based on the halfspace depth function are shown to generalize versions introduced by P. J. Bickel and E. L. Lehmann (1976, 1979) in the univariate case and by M. L. Eaten (1982) and H. Oja (1983) in the multivariate cast. Scatter measures are also discussed. with emphasis on those based on the halfspace depth. Basic desirable properties established for the previous versions of more scattered are shown to carry over to the depth-based notions as well, in both the univariate and the multivariate cases. Further, some properties unique to the depth-based notions are established. (C) 2000 Academic Press.

[发布日期] 2000-10-01

[关键词] scatter measure;more scattered;statistical depth functions;multivariate;nonparametric;statistical inference;halfspace depth