English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Density level sets can be estimated using plug-in methods, excess massalgorithms or a hybrid of the two previous methodologies. The plug-inalgorithms are based on replacing the unknown density by some nonparametricestimator, usually the kernel. Thus, the bandwidth selection is a fundamentalproblem from an applied perspective. However, if some a priori informationabout the geometry of the level set is available, then excess mass algorithmscould be useful. Hybrid methods such that granulometric smoothing algorithmassume a mild geometric restriction on the level set and it requires a pilotnonparametric estimator of the density. In this work, a new hybrid algorithm isproposed under the assumption that the level set is r-convex. The main problemin practice is that r is an unknown geometric characteristic of the set. Astochastic algorithm is proposed for selecting its optimal value. The resultingdata-driven reconstruction of the level set is able to achieve the sameconvergence rates as the granulometric smoothing method. However, they do nodepend on any penalty term because, although the value of the shape index r isa priori unknown, it is estimated in a data-driven way from the sample points.The practical performance of the estimator proposed is illustrated through areal data example.

A fully data-driven method for estimating density level sets