Kernel estimation of density level sets

By Benoît Cadre. 2005

114 citations recorded by the source corpus.

Let f be a multivariate density and f"n be a kernel estimate of f drawn from the n-sample X"1,...,X"n of i.i.d. random variables with density f. We compute the asymptotic rate of convergence towards 0 of the volume of the symmetric difference between the t-level set {f>=t} and its plug-in estimator {f"n>=t}. As a corollary, we obtain the exact rate of convergence of a plug-in-type estimate of the density level set corresponding to a fixed probability for the law induced by f.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/e1d2e52761feceae9b293f278121cb4e01e70ccc

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In Artificial Intelligence

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Citations in the corpus

Distribution Free Prediction Sets (2013, methodology): “In this article, we will use σi = p̂(Yi) where p̂ is an appropriate density estimator.”
PLUG‐IN ESTIMATION OF GENERAL LEVEL SETS (2006, background): “A sharp optimality result has been obtained by Cadre (2004).”
Set estimation: another bridge between statistics and geometry (2009, methodology): “The reach condition was introduced by Federer (1959) to get an interesting generalization of Steiner's theorem: This result establishes that for a compact convex set, the volume function V (2) = μ(B(S, 2)) is a polynomial in 2 of order d.”
An Introduction to Topological Data Analysis: Fundamental and Practical Aspects for Data Scientists (2017, background): “, Cang and Wei (2017). The above mentioned kernels and vector summaries of persistence diagrams are built independently of the considered data analysis or learning task. Moreover, it appears that in many cases the relevant topological information is not carried by the whole persistence diagrams but ”
Topological Data Analysis (2016, background): “The theoretical properties of the estimator L̂t are discussed, for example, in Cadre (2006) and Rinaldo & Wasserman (2010).”