On depth and deep points: a calculus

By Ivan Mizera. 2002

129 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/208d952d44352dc4eab72c98570387a7c9ca900c

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In Statistics and Probability

Citations in the corpus

Location–Scale Depth (2004, methodology): “The new depth is introduced in Section 3 as an instance of the general theory of halfspace depth elaborated by Mizera (2002), based on the idea outlined by Rousseeuw and Hubert (1999).”
Robust estimation via robust gradient estimation (2018, methodology): “…have been developed that are optimally robust for a variety of inferential tasks, including hypothesis testing (Huber, 1965), mean estimation (Mizera, 2002), general parametric estimation (Yatracos, 1985; Donoho and Liu, 1988; Chen et al., 2016) and non-parametric estimation (Devroye and…”
General notions of statistical depth function (2000, background): “Mizera (1998) has introduced a differential calculus for depth functions.”
Choosing Among Notions of Multivariate Depth Statistics (2020, background): “Finally, a more general view on depth as depth of a fit is discussed, which yields extensions beyond locational depth such as regression depth (Rousseeuw and Hubert, 1999) and tangent depth (Mizera, 2002).”
QUASI-CONCAVE DENSITY ESTIMATION (2010, background): “enjoyed a considerable vogue with important contributions of Walther (2001, 2002, 2009), Pal, Woodroofe and Meyer (2007), Rufibach (2007), Dümbgen and Rufibach (2009), Balabdaoui, Rufibach and Wellner (2009), Chang and Walther (2007), and Cule, Samworth and Stewart (2010b), among others.”
Quantile tomography: using quantiles with multivariate data (2008, background): “Other references are Donoho and Gasko (1992), Rousseeuw and Hubert (1999), Rousseeuw and Ruts (1999), and Mizera (2002).”
On Maximum Depth and Related Classifiers (2005, background): “Various other well-known depth functions such as likelihood depth, convex hull peeling depth and zonoid depth have been studied by Liu et al. (1999), Zuo & Serfling (2000a,b), Mosler (2002) and Mizera (2002).”
Adaptive Huber Regression (2017, background): “Significant contributions have also been made in Liu (1990), Liu, Parelius, and Singh (1999), Zuo and Serfling (2000), Mizera (2002), and Mizera and Müller (2004).”
Depth and homogeneity in regional flood frequency analysis (2008, background): “The depth function is a statistical notion developed in the seventies and which receives increasing interest [e.g., Tukey, 1975; Liu, 1990; Liu and Singh, 1993; Rousseeuw and Hubert, 1999; Zuo and Serfling, 2000; Mizera, 2002; Mizera and Müller.”
Robust regression via mutivariate regression depth (2017, methodology): “We refer the readers to [25, 2, 29, 31, 1] for other important properties.”