Compositional regression with functional response

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F18%3A73589345" target="_blank" >RIV/61989592:15310/18:73589345 - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S0167947318300276" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0167947318300276</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.csda.2018.01.018" target="_blank" >10.1016/j.csda.2018.01.018</a>

Result language
angličtina
Original language name
Compositional regression with functional response
Original language description
The problem of performing functional linear regression when the response variable is represented as a probability density function (PDF) is addressed. PDFs are interpreted as functional compositions, which are objects carrying primarily relative information. In this context, the unit integral constraint allows to single out one of the possible representations of a class of equivalent measures. On these bases, a function-on-scalar regression model with distributional response is proposed, by relying on the theory of Bayes Hilbert spaces. The geometry of Bayes spaces allows capturing all the key inherent features of distributional data (e.g., scale invariance, relative scale). A B-spline basis expansion combined with a functional version of the centered log-ratio transformation is utilized for actual computations. For this purpose, a new key result is proved to characterize B-spline representations in Bayes spaces. The potential of the methodological developments is shown on simulated data and a real case study, dealing with metabolomics data. A bootstrap-based study is performed for the uncertainty quantification of the obtained estimates.
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/GA15-06991S" target="_blank" >GA15-06991S: Functional data analysis and related topics</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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