On the Concept of Depth for Functional Data

By Sara López-Pintado, Juan Romo. 2009

613 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/ae67b341dbffd04d883b831bf77179cf710bbeec

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In Statistics and Probability

Citations in the corpus

Outlier detection in functional data by depth measures, with application to identify abnormal NOx levels (2008, background): “Recently, the notion of depth has been extended to functional data by Fraiman and Muniz (2001) and Cuevas et al. (2006, 2007) (see also, López-Pintado and Romo (2006), for an alternative point of view based on the graphic representation of curves).”
Assessing the Calibration of High-Dimensional Ensemble Forecasts Using Rank Histograms (2013, methodology): “1 Band depth rank López-Pintado and Romo (2009) introduce a center-outward ordering of curves which they call band depth.”
Flexible semiparametric generalized Pareto modeling of the entire range of rainfall amount (2019, neutral): “These type of boxplots use the band depth introduced by López-Pintado and Romo (2009) to order the functions.”
Multivariate Functional Halfspace Depth (2014, methodology): “Our depth-based approach allows to visualize this dispersion by means of the central regions, introduced in López-Pintado and Romo (2009).”
Distribution and quantile functions, ranks and signs in dimension d: A measure transportation approach (2021, background): “…(2006), Zuo and Serfling (2000), among others; see Serfling (2002) for a general introduction on statistical depth, Hallin et al. (2010) for the related concept of quantile, Lòpez-Pintado and Romo (2012) for functional extensions, Zuo (2018) for a state-of-the art survey in a regression context.”
On data depth in infinite dimensional spaces (2014, methodology): “MBD and MHRD for probability distributions in C[0, 1], as defined by López-Pintado and Romo (2009, 2011), are given below.”
Integrated depth for functional data: statistical properties and consistency (2016, methodology): “This class includes the band depth (see [23]), half-region depth (cf.”
The spatial distribution in infinite dimensional spaces and related quantiles and depths (2014, background): “rsion is given by SDd(x) = 1−||Sb x||. Here, S x and Sb x are as deﬁned in Section 2. There are a few other notions of depth function for data in inﬁnite dimensional function spaces (see, e.g., [16], [24], [25] and [31]). However, as shown in [9], some of these depth functions exhibit degeneracy for”
Rainbow Plots, Bagplots, and Boxplots for Functional Data (2010, methodology): “Notable exceptions are the phase-plane plot of Ramsay and Ramsey (2002) and the rug plot of Hyde, Jank, and Shmueli (2006), which highlight important distributional characteristics from the first and second derivatives of functional data.”
Global envelope tests for spatial processes (2013, methodology): “…is closely connected to the methods that are used in functional data analysis, where measures of functional depth are typically used to describe the centrality of a curve among a set of curves (e.g. Ramsay and Silverman (2006), Ramsay et al. (2009) and López-Pintado and Romo (2009, 2011)).”