Level sets of depth measures in abstract spaces Level sets of depth measures in abstract spaces

The lens depth of a point has been recently extended to general metric spaces, which is not the case for most depths. It is defined as the probability of being included in the intersection of two random balls centred at two random points X and Y , with the same radius d ( X , Y ). We prove that, on...

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Vydáno v:	Test (Madrid, Spain) Ročník 32; číslo 3; s. 942 - 957
Hlavní autoři:	Cholaquidis, A., Fraiman, R., Moreno, L.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2023
Témata:	Economics Finance Insurance Management Mathematics and Statistics Original Paper Statistical Theory and Methods Statistics Statistics for Business 62G05 62R20 Lens depth Phylogenetic tree Metric spaces Level sets Depth measures 62G35
ISSN:	1133-0686, 1863-8260
On-line přístup:	Získat plný text
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Shrnutí:	The lens depth of a point has been recently extended to general metric spaces, which is not the case for most depths. It is defined as the probability of being included in the intersection of two random balls centred at two random points X and Y , with the same radius d ( X , Y ). We prove that, on a separable and complete metric space, the level sets of the empirical lens depth based on an iid sample, converge in the Painlevé–Kuratowski sense, to its population counterpart. We also prove that, restricted to compact sets, the empirical level sets and their boundaries are consistent estimators, in Hausdorff distance, of their population counterparts, and analyse two real-life examples.
Bibliografie:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23
ISSN:	1133-0686 1863-8260
DOI:	10.1007/s11749-023-00858-x