Consistency of non-integrated depths for functional data

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F15%3A10313707" target="_blank" >RIV/00216208:11320/15:10313707 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.jmva.2015.05.012" target="_blank" >http://dx.doi.org/10.1016/j.jmva.2015.05.012</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jmva.2015.05.012" target="_blank" >10.1016/j.jmva.2015.05.012</a>

Result language
angličtina
Original language name
Consistency of non-integrated depths for functional data
Original language description
In the analysis of functional data, the concept of data depth is of importance. Strong consistency of a sample version of a data depth is among the basic statistical properties that need to hold. In this paper we discuss consistency properties of three popular types of functional depth: the band depth, the half-region depth and the infimal depth. The latter is a special case of the recently introduced general class of Phi-depths. All three considered depth functions are of a non-integrated type. Counterexamples illustrate some problems with consistency results for these data depths. The main contribution of this paper consists of providing sufficient conditions for consistency of these non-integrated data depths to hold.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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