General notions of statistical depth function

By Yijun Zuo, Robert Serfling. 2000

1,001 citations recorded by the source corpus.

Subfields: Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/0a7c6b5bf035199b2054d8822b6e36534022b664

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In Management Science and Operations Research

In Statistics and Probability

Citations in the corpus

Nonparametric Phase-II control charts for monitoring high-dimensional processes with unknown parameters (2020, background): “See, Zuo and Serfling (2000), Qiu (2013), among others, for more details on data-depths.”
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).”
Choosing Among Notions of Multivariate Depth Statistics (2020, background): “Many properties of Mahalanobis, Lp-, halfspace, simplicial, projection, and Oja depth are demonstrated in Zuo and Serfling (2000).”
Multivariate Rank-Based Distribution-Free Nonparametric Testing Using Measure Transportation (2019, background): “…ranks, e.g., Bickel 1965; Puri and Sen 1966; spatial ranks, e.g., Chaudhuri 1996; Marden 1999; depth-based ranks, e.g., Liu and Singh 1993; Zuo and Serfling 2000; Mahalanobis ranks, e.g., Hallin and Paindaveine 2004, 2006) and the corresponding rank-based tests no longer possess exact…”
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.”
An Approach to Multivariate Covariate-Dependent Quantile Contours With Application to Bivariate Conditional Growth Charts (2008, methodology): “…space, there is no universally preferred definition of multivariate quantiles, but various ideas have been developed in the literature; for example, Liu, Parelius, and Singh (1999) and Zuo and Serfling (2000) used multivariate quantile functions based on the half-space depth function.”
Robust estimation and classification for functional data via projection-based depth notions (2007, methodology): “A projection-based method is proposed in Zuo (2003); see also Zuo and Serfling (2000) .”
Robust covariance and scatter matrix estimation under Huber’s contamination model (2015, background): “Zuo and Serfling [52] advocated the notion of statistical depth function that satisfies the four properties in [29] and verified that Tukey’s depth indeed satisfies all these properties while many other depth functions [29, 37, 38, 44] do not.”
A nonparametric multivariate multisample test based on data depth (2012, methodology): “Several properties of the halfspace depth discussed by Donoho and Gasko (1992), Rousseeuw and Ruts (1999), Small (1987), Zuo and Serfling (2000).”
Assessing probabilistic forecasts of multivariate quantities, with an application to ensemble predictions of surface winds (2008, background): “Viewed slightly differently, the MST rank provides a center-outward ordering for the combined set of ensemble members and the observation, similarly to the way in which statistical depth functions operate (Zuo and Serfling 2000).”
Some intriguing properties of Tukey's half-space depth (2012, background): “In fact, it satisfies all four of the desirable properties of depth functions first mentioned in [12] and subsequently investigated in [22], namely, affine invariance, maximality at the center, monotonicity with respect to the deepest point and vanishing at infinity.”
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.”
Integrated depth for functional data: statistical properties and consistency (2016, background): “For the halfspace depth function Properties (D1), (D2), (D3) and (D4) hold true for each Q ∈ P (RK), as was shown by Zuo and Serfling ([39], Thm.”
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 .”