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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Important information concerning a multivariate data set, such as clustersand modal regions, is contained in the derivatives of the probability densityfunction. Despite this importance, nonparametric estimation of higher orderderivatives of the density functions have received only relatively scantattention. Kernel estimators of density functions are widely used as theyexhibit excellent theoretical and practical properties, though theirgeneralization to density derivatives has progressed more slowly due to themathematical intractabilities encountered in the crucial problem of bandwidth(or smoothing parameter) selection. This paper presents the first fullyautomatic, data-based bandwidth selectors for multivariate kernel densityderivative estimators. This is achieved by synthesizing recent advances inmatrix analytic theory which allow mathematically and computationally tractablerepresentations of higher order derivatives of multivariate vector valuedfunctions. The theoretical asymptotic properties as well as the finite samplebehaviour of the proposed selectors are studied. {In addition, we explore indetail the applications of the new data-driven methods for two otherstatistical problems: clustering and bump hunting. The introduced techniquesare combined with the mean shift algorithm to develop novel automatic,nonparametric clustering procedures which are shown to outperform mixture-modelcluster analysis and other recent nonparametric approaches in practice.Furthermore, the advantage of the use of smoothing parameters designed fordensity derivative estimation for feature significance analysis for bumphunting is illustrated with a real data example.

Data-driven density derivative estimation, with applications to nonparametric clustering and bump hunting