Structural properties and convergence results for contours of sample statistical depth functions
Zuo, Yijun ; Serfling, Robert
Ann. Statist., Tome 28 (2000) no. 3, p. 483-499 / Harvested from Project Euclid
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Statistical depth functions have become increasingly used in nonparametric inference for multivariate data. Here the contours of such functions are studied. Structural properties of the regions enclosed by contours, such as affine equivariance, nestedness, connectedness and compactness, and almost sure convergence results for sample depth contours, are established. Also, specialized results are established for some popular depth functions, includinghalfspace depth, and for the case of elliptical distributions. Finally, some needed foundational results on almost sure convergence of sample depth functions are provided.
Publié le : 2000-04-15
Classification:  Statistical depth functions,  depth contours,  sample depth contours,  almost sure convergence,  halfspace depth,  elliptical distributions,  62H12,  62G20 
@article{1016218227,
     author = {Zuo, Yijun and Serfling, Robert},
     title = {Structural properties and convergence results for contours of
		 sample statistical depth functions},
     journal = {Ann. Statist.},
     volume = {28},
     number = {3},
     year = {2000},
     pages = { 483-499},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1016218227}
}

Zuo, Yijun; Serfling, Robert. Structural properties and convergence results for contours of
		 sample statistical depth functions. Ann. Statist., Tome 28 (2000) no. 3, pp.  483-499. http://gdmltest.u-ga.fr/item/1016218227/