Simplicial depth: Characterization and reconstruction

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F23%3A10472210" target="_blank" >RIV/00216208:11320/23:10472210 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=dLcO_~uWFT" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=dLcO_~uWFT</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1002/sam.11618" target="_blank" >10.1002/sam.11618</a>

Result language
angličtina
Original language name
Simplicial depth: Characterization and reconstruction
Original language description
Statistical depth functions have been designed with the intention of extending nonparametric inference toward multivariate setups. As such, the depths should serve as multivariate analogues of the quantile functions known from the analysis of real-valued data. The so-called characterization and reconstruction questions are among the fundamental open problems of the contemporary depth research. Roughly speaking, they ask: (a) Is it is possible that two different datasets, or more generally, two different probability distributions, correspond to identical depths, or does the depth function uniquely characterize the underlying distribution? (b) Knowing a depth function, can we reconstruct the corresponding distribution? For any given depth to constitute a fully-fledged alternative to the quantile function, the depth must characterize wide classes of probability measures, and these measures must be simple to recover from their depths. We investigate these characterization/reconstruction questions for the classical simplicial depth for multivariate data. We show that, under mild conditions, datasets (represented by measures putting equal mass 1/n$$ 1/n $$ to each datum in a dataset of size n$$ n $$) and atomic measures are characterized by, and can be easily reconstructed from, their simplicial depth.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10103 - Statistics and probability

Project
<a href="/en/project/GX19-28231X" target="_blank" >GX19-28231X: DyMoDiF - Dynamic Models for the Digital Finance</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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