Compositional regression with functional response

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Compositional regression with functional response

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Compositional regression with functional response

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10103 - Statistics and probability

Projekt

<a href="/cs/project/GA15-06991S" target="_blank" >GA15-06991S: Analýza funkcionálních dat a související témata</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2018

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

COMPUTATIONAL STATISTICS &amp; DATA ANALYSIS

ISSN

0167-9473

e-ISSN

—

Svazek periodika

123

Číslo periodika v rámci svazku

JUL

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

20

Strana od-do

66-85

Kód UT WoS článku

000430147700005

EID výsledku v databázi Scopus

2-s2.0-85042492763