Asymptotics and optimal bandwidth selection for highest density region estimation

By Richard J. Samworth, Matt P. Wand. 2010

60 citations recorded by the source corpus.

We study kernel estimation of highest density regions (HDR). Our main contributions are twofold. Firstly, we derive a uniform-in-bandwidth asymptotic approximation to a risk that is appropriate for HDR estimation. This approximation is then used to derive a bandwidth selection rule for HDR estimation possessing attractive asymptotic properties. We also present the results of numerical studies that illustrate the benefits of our theory and methodology.

Subfields: Computer Vision and Pattern Recognition, Numerical Analysis, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/87de6f7c9a91441fd64b6ea07bf740480d433157

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In Computer Vision and Pattern Recognition

In Numerical Analysis

In Statistics and Probability

Citations in the corpus

Distribution Free Prediction Sets (2013, background): “Bandwidth selection for level sets is discussed in Samworth and Wand (2010).”
Optimal weighted nearest neighbour classifiers (2011, background): “roved that in a certain sense this is the minimax optimal rate. Further related work includes the literature on highest density region or level set estimation (Polonik, 1995; Rigollet and Vert, 2009; Samworth and Wand, 2010). Hall and Samworth (2005) and Biau and Devroye (2010) proved an analogous r”
A Review on Modal Clustering (2016, background): “Among them, we like to mention the contribution of Samworth & Wand (2010) who propose a plug-in bandwidth selection rule tailored for high-density regions estimation and possessing attractive asymptotic properties.”