Structural properties and convergence results for contours of sample statistical depth functions

By Yijun Zuo, Robert Serfling. 2000

180 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/d969bd12762ab62f76c3ae72a48e36165856b2d3

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In Statistics and Probability

Citations in the corpus

Location–Scale Depth (2004, background): “Theorem 7 implies the convergence of depth contours via theorem 4.1 of Zuo and Serfling (2000b), which extends the results of He and Wang (1997).”
A Depth Function and a Scale Curve Based on Spatial Quantiles (2002, background): “In turn, by Theorem 4.1 of Zuo and Serfling (2000b), this yields almost sure convergence of the central regions, CFn(r) → CF (r) a.s., provided that the boundary {x : ‖Q−1F (x)‖ = r} of CF (r) has F -probability 0.”
Multivariate Functional Halfspace Depth (2014, methodology): “In Theorem 1 we show that the multivariate functional depth satisfies some key properties, adapted to a functional data context that were put forward by Zuo and Serfling (2000a).”
Depth weighted scatter estimators (2005, background): “The projection depth of a point x ∈Rd with respect to a given distribution F of a random vector X ∈Rd, PD(x,F ), is defined as [Zuo and Serfling (2000a) and Zuo (2003)] PD(x,F ) = 1/(1 +O(x,F )),(8) where the outlyingness O(x,F ) = sup‖u‖=1 (u ′x− µ(Fu))/σ(Fu), and Fu is the distribution of u′X .”
Multivariate spacings based on data depth: I. Construction of nonparametric multivariate tolerance regions (2008, background): “More discussion on different notions of data depth can be found in [17, 31].”
On Maximum Depth and Related Classifiers (2005, background): “For SVDd, if one has the additional condition d ‡ 1, the same assertion holds (see e.g. Zuo & Serfling, 2000a).”
On the Concept of Depth for Functional Data (2009, background): “Liu (1990) and Zuo and Serfling (2000a) introduced and studied key properties a depth should satisfy.”
General notions of statistical depth function (2000, methodology): “Then it is not difficult to verify, based on results established in Zuo and Serfling (2000c), that X is H-symmetric about θ, which is thus the center of the distribution.”