On smoothness of Tukey depth contours

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F16%3A10329015" target="_blank" >RIV/00216208:11320/16:10329015 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1080/02331888.2016.1145680" target="_blank" >http://dx.doi.org/10.1080/02331888.2016.1145680</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1080/02331888.2016.1145680" target="_blank" >10.1080/02331888.2016.1145680</a>

Result language
angličtina
Original language name
On smoothness of Tukey depth contours
Original language description
The smoothness of Tukey depth contours is a regularity condition often encountered in asymptotic theory, among others. This condition ensures that the Tukey depth fully characterizes the underlying multivariate probability distribution. In this paper we demonstrate that this regularity condition is rarely satisfied. It is shown that even well-behaved probability distributions with symmetrical, smooth and (strictly) quasi-concave densities may have non-smooth Tukey depth contours, and that the smoothness behaviour of depth contours is fairly unpredictable.
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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Project
<a href="/en/project/GBP402%2F12%2FG097" target="_blank" >GBP402/12/G097: DYME-Dynamic Models in Economics</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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