Robust functional estimation using the median and spherical principal components

By Daniel Gervini. 2008

135 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/f5b994e24fb6cea94b7fc920fcab349bb5f3cc8e

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In Statistics and Probability

Citations in the corpus

Dispersion operators and resistant second-order functional data analysis (2012, background): “On the other hand, Gervini (2008) needed no moment assumptions, whereas we need to assume finite second moments: without moment assumptions the convergence of an infinite Karhunen–Loève series is not guaranteed, while a finite sum is always well defined regardless of the properties of the random…”
Modeling and forecasting electricity spot prices: A functional data perspective (2013, methodology): “This approach is similar to robust estimation procedures proposed by Locantore et al. (1999) and Gervini (2008) but differs conceptually insofar as we do not consider any functional observation Xt as an outlier.”
The spatial distribution in infinite dimensional spaces and related quantiles and depths (2014, methodology): “The author of [17] proposed an algorithm for computing the sample spatial median in Hilbert spaces.”
Functional Data Analysis (2016, methodology): “…and contamination and more generally visual exploration of functional data include exploratory box plots (Hyndman & Shang 2010; Sun & Genton 2011) and robust versions of FPCA (Crambes, Delsol & Laksaci 2008; Gervini 2008; Bali et al. 2011; Kraus & Panaretos 2012; Boente & Salibi´an-Barrera 2014).”
Robust functional principal components: A projection-pursuit approach (2011, methodology): “Gervini (2008) proved the Fisher-consistency of the eigenfunctions of the spatial covariance operator, but under the additional assumption that X has a finite Karhunen–Loève expansion so that V has only a finite number of nonzero eigenvalues, which is essentially the multivariate setting.”
Elliptical graphical modelling (2011, methodology): “)), and thus its use has been proposed for such kind of multivariate analysis that is based on this information only, most notably principal component analysis, (Marden, 1999; Locantore et al., 1999; Croux et al., 2002; Gervini, 2008).”
Second-Order Comparison of Gaussian Random Functions and the Geometry of DNA Minicircles (2010, methodology): “For this reason, we pursue a robust analysis for the mean curve using a functional median introduced in Gervini (2008).”
Testing the Equality of Covariance Operators in Functional Samples (2011, background): “M E ] 2 point for many functional data analysis procedures, Reiss & Ogden (2007), Gervini (2008), Yao & Müller (2010), Gabrys et al. (2010) are just a handful of illustrative references.”
A survey of functional principal component analysis (2014, background): “Gervini ( 2008 ) proposed a fully functional robust estimators which are functional versions of the multivariate median and spherical principal components ( see also Locantore et al .”