On boundary estimation

By Antonio Cuevas, A. Rodr'iguez-Casal. Advances in Applied Probability, 2004

151 citations recorded by the source corpus.

Subfields: Applied Mathematics, Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/9f18409e7bf7ae7a6ed5ac070bb093c22310a7f5

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In Applied Mathematics

In Artificial Intelligence

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Citations in the corpus

Set estimation: another bridge between statistics and geometry (2009, methodology): “This problem has been considered in Cuevas and Rodríguez-Casal (2004); see subsection 3.3 below.”
Kernel estimation of density level sets (2005, background): “One may find in the literature many types of estimators, such as the plug-in estimators (Baillo, Cuesta-Albertos and Cuevas [10], Baillo [11], Cuevas and Fraiman [7], Molchanov [12,13]), the estimators defined by an excess mass approach (Hartigan [14], Muller [15], Muller and Sawitzki [16], Nolan [1”
Statistical Analysis and Parameter Selection for Mapper (2017, methodology): “This assumption is popular in the literature about set estimation (see for instance Cuevas, 2009; Cuevas and Rodŕıguez-Casal, 2004).”
On Statistical Properties of Sets Fulfilling Rolling-Type Conditions (2011, background): “[2], [9], and [29] for some results on boundary estimation.”
Topological Consistency via Kernel Estimation (2014, methodology): “ closed balls around the sample points U(X,r):= [ X∈X Br(X), (3.2) for some choice of radius r (cf. [12, 58]). In the level-set estimation literature, this procedure is known as the “naive” estimator [28, 32, 72]. We can use this idea to estimate the homology of the set DL using the following proced”
Convex geometry of max-stable distributions (2006, methodology): “ample continuous random functions. Although statistical estimation issues are left outside the scope of the current paper, note that it may be possible to use techniques from set-estimation (see e.g. [6, 17, 21]) in order to estimate the dependency set and thereupon arrive at new estimators for the ”
Set estimation under convexity type assumptions (2007, methodology): “Now the result is an immediate consequence of Theorem 3 in Cuevas and Rodríguez-Casal [7] where it is proved that if S is compact and standard with respect to PX then dH (Xn, S) = O((logn/n)1/d).”
A nonparametric approach to the estimation of lengths and surface areas (2007, methodology): “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 ”
An Introduction to Topological Data Analysis: Fundamental and Practical Aspects for Data Scientists (2017, methodology): “In the paper Niyogi et al. (2008), it is shown that the homotopy type of Riemannian manifolds with reach larger than a given constant can be recovered with high probability from offsets of a sample on (or close to) the manifold.”