Total Error in a Plug-in Estimator of Level Sets

By Amparo Baíllo. 2003

50 citations recorded by the source corpus.

Subfields: Applied Mathematics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/5a30240fb1a12a3ec55721e03792b281bc8bebb0

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In Applied Mathematics

In Statistics and Probability

Citations in the corpus

Optimal rates for plug-in estimators of density level sets (2006, background): “Related papers are Báıllo et al. (2001) and Báıllo (2003), which investigate plug-in estimators based on a certain type of kernel density estimate.”
A nonparametric approach to the estimation of lengths and surface areas (2007, background): “In a way, the length and surface area estimation problem can be seen as a further, more difficult, stage in set estimation theory, after the early developments concerned with the estimation of volume (associated with the L1 (measure) distance; see [8]), “visual” shape (associated with the Hausdorff ”
A Review on Modal Clustering (2016, background): “Further references are Tsybakov (1997), Walther (1997), Cuevas et al. (2000), Baíllo et al. (2000), Baíllo et al. (2001), Baíllo (2003), Rigollet & Vert (2009) and Mason & Polonik (2009), and references therein, which delineate conditions, rates of convergence and further asymptotic results for a…”
Distribution Free Prediction Sets (2013, background): “When t is given, consistent estimators of L(t) and rates of convergence have been studied in detail (Polonik 1995; Tsybakov 1997; Baillo, Cuestas-Alberto, and Cuevas 2001; Baillo 2003; Cadre 2006; Willett and Nowak 2007; Rigollet and Vert 2009; Rinaldo and Wasserman 2010).”
Kernel estimation of density level sets (2005, background): “Under various assumptions, Baíllo [11], Baíllo, Cuesta-Albertos and Cuevas [10], and Cuevas and Fraiman [7] obtained some rates of convergence.”
Asymptotic normality of plug-in level set estimates. (2009, background): “Relevant published work (not yet mentioned above) include Hartigan (1987), Polonik (1995), Cavalier (1997), Tsybakov (1997), Walther (1997), Báıllo, Cuevas and Justel (2000), Báıllo, Cuestas-Albertos and Cuevas (2001), Cuevas, Febrero and Fraiman (2000), Báıllo (2003), Tsybakov (2004), Steinwart, Hu”
Asymptotics and optimal bandwidth selection for highest density region estimation (2010, background): “Contributions include Hartigan (1987), Müller and Sawitzki (1991), Polonik (1995), Hyndman (1996), Tsybakov (1997), Baíllo, Cuesta-Albertos and Cuevas (2001), Baíllo (2003), Cadre (2006), Jang (2006), Rigollet and Vert (2009) and Mason and Polonik (2009).”