Convergence rates in nonparametric estimation of level sets

By Amparo Baíllo, Juan Antonio Cuesta-Albertos, Antonio Cuevas. 2001

63 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/c1538698abbeb01b1bce1a34d52a34b34f239628

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Statistics and Probability

Citations in the corpus

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.”
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…”
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.”
Topological Consistency via Kernel Estimation (2014, methodology): “the support ofa distribution and its boundaryis used for measuringeﬃciency). Various solutions have been proposed to the level set estimation problem. Standard solutions include the plug-in estimator [4, 5, 27, 51, 52], the excess mass estimator [42, 53, 54, 60, 63, 68], and the “naive” estimator [2”