Robust estimation and classification for functional data via projection-based depth notions

By Antonio Cuevas, M. Febrero–Bande, Ricardo Fraiman. Computational statistics (Zeitschrift), 2007

328 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/64c89bc1aec45637e43fc98434b78ed161ad1ca1

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Citations in the corpus

Outlier detection in functional data by depth measures, with application to identify abnormal NOx levels (2008, background): “See Cuevas et al. (2007) for a detailed exposition of the random projection depth.”
Componentwise classification and clustering of functional data (2012, background): “…and Pertega (2004), Biau et al. (2005), Fromont and Tuleau (2006), Leng and Müller (2006), LópezPintado and Romo (2006), Rossi and Villa (2006), Cuevas et al. (2007), Wang et al. (2007), Berlinet et al. (2008), Epifanio (2008), Peng and Müller (2008), Araki et al. (2009) and Chamroukhi et…”
Achieving near perfect classification for functional data (2012, background): “…classification rule, Leng and Müller (2006) and Chamroukhi et al. (2010), who introduced model-based classifiers, López-Pintado and Romo (2006) and Cuevas et al. (2007), who suggested classifiers based on the notion of data depth, Rossi and Villa (2006), who developed methodology founded on the…”
On data depth in infinite dimensional spaces (2014, background): “For a random element X and a fixed element x in L2[0, 1], the h-depth introduced in Cuevas et al. (2007) is defined as E{Kh(||x−X||)}, where Kh(t) = h−1 K (t/h) for some fixed kernel K and h > 0 is a tuning parameter.”
Multivariate Functional Halfspace Depth (2014, methodology): “A well-studied situation is the addition of the first order derivatives which provides additional information on the shape of the curves and consequently is interesting to detect curves with an outlying shape (Cuevas et al., 2007).”
Robust functional estimation using the median and spherical principal components (2008, methodology): “In this context, we can mention the trimmed means proposed by Fraiman & Muniz (2001) and the depth-based estimators of Cuevas et al. (2007) and Lopez-Pintado & Romo (2007).”
Depth Statistics (2012, methodology): “Functional data depth is applied to similar tasks in description, classification and testing; see e.g. López-Pintado and Romo (2009); Cuevas et al. (2007).”
Efficient and fast estimation of the geometric median in Hilbert spaces with an averaged stochastic gradient algorithm (2011, background): “[10] have proposed random projection techniques in the context of maximal depth estimators and studied their properties via simulation studies.”
On the Concept of Depth for Functional Data (2009, background): “Recently, Cuevas, Febrero, and Fraiman (2007) have proposed a projection-based depth for functions.”
Statistical Computing in Functional Data Analysis: The R Package fda.usc (2012, methodology): “Undoubtedly, package fda (Ramsay, Wickham, Graves, and Hooker 2012) is a basic reference to work in R programming environment (R Development Core Team 2012) with functional data. The books by Ramsay and Silverman (2005) and Ramsay and Silverman (2002) are well-known references in this field. In both”
Classification Using Censored Functional Data (2013, background): “See for example Hall et al. (2001), Ferraty and Vieu (2003), Glendinning and Herbert (2003), Vilar and Pertega (2004), Biau et al.”