Bandwidth selection for kernel density estimators of multivariate level sets and highest density regions

Doss, Charles R.; Weng, Guangwei

doi:10.48550/arxiv.1806.00731

Cited by 2 publications

(2 citation statements)

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“…The proof of Theorem 3 is given in Appendix C. The set difference is a conventional measure of the difference between two sets. Applying the probability P GPS to the set difference is a common measure of the convergence of a set estimator (Mason and Polonik, 2009;Rigollet and Vert, 2009;Qiao, 2017;Doss and Weng, 2018). Theorem 3 shows that A π 0 and A π 0 +π 1 are consistent estimators of A and A ∪ R, respectively.…”

Section: Persistence Curvesmentioning

confidence: 99%

Measuring human activity spaces from GPS data with density ranking and summary curves

Chen¹,

Dobra²

2020

Ann. Appl. Stat.

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Activity spaces are fundamental to the assessment of individuals' dynamic exposure to social and environmental risk factors associated with multiple spatial contexts that are visited during activities of daily living. In this paper we survey existing approaches for measuring the geometry, size and structure of activity spaces based on GPS data, and explain their limitations. We propose addressing these shortcomings through a nonparametric approach called density ranking, and also through three summary curves: the mass-volume curve, the Betti number curve, and the persistence curve. We introduce a novel mixture model for human activity spaces, and study its asymptotic properties. We prove that the kernel density estimator which, at the present time, is one of the most widespread methods for measuring activity spaces is not a stable estimator of their structure. We illustrate the practical value of our methods with a simulation study, and with a recently collected GPS dataset that comprises the locations visited by ten individuals over a six months period.MSC 2010 subject classifications: Primary 62G07; secondary 62P25, 91C99

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Section: Persistence Curvesmentioning

confidence: 99%

Measuring human activity spaces from GPS data with density ranking and summary curves

Chen¹,

Dobra²

2020

Ann. Appl. Stat.

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“…So far, the aim of choosing an amount of smoothing for the specific task of highlighting clustering structures has been scarcely pursued in literature. A related idea, although without particular reference to cluster analysis, has been developed by [35], who propose a plug-in type bandwidth selector appropriate for estimation of highest density regions (see also [31] and [14]). Another related work, more focused on the clustering problem, is the one by [15], where the author suggests to consider the self-coverage measure as a criterion for bandwidth selection.…”

Section: Asymptotic Bandwidth Selection For Modal Clusteringmentioning

confidence: 99%

Modal clustering asymptotics with applications to bandwidth selection

Casa¹,

Chacón²,

Menardi³

2020

Electron. J. Statist.

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Density-based clustering relies on the idea of linking groups to some specific features of the probability distribution underlying the data. The reference to a true, yet unknown, population structure allows to frame the clustering problem in a standard inferential setting, where the concept of ideal population clustering is defined as the partition induced by the true density function. The nonparametric formulation of this approach, known as modal clustering, draws a correspondence between the groups and the domains of attraction of the density modes. Operationally, a nonparametric density estimate is required and a proper selection of the amount of smoothing, governing the shape of the density and hence possibly the modal structure, is crucial to identify the final partition. In this work, we address the issue of density estimation for modal clustering from an asymptotic perspective. A natural and easy to interpret metric to measure the distance between density-based partitions is discussed, its asymptotic approximation explored, and employed to study the problem of bandwidth selection for nonparametric modal clustering.

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Bandwidth selection for kernel density estimators of multivariate level sets and highest density regions

Cited by 2 publications

References 0 publications

Measuring human activity spaces from GPS data with density ranking and summary curves

Measuring human activity spaces from GPS data with density ranking and summary curves

Modal clustering asymptotics with applications to bandwidth selection

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