Statistical Analysis of Bivariate Densities with Compositional Splines

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F25%3A73634021" target="_blank" >RIV/61989592:15310/25:73634021 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1007/978-3-031-92383-8_60" target="_blank" >http://dx.doi.org/10.1007/978-3-031-92383-8_60</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/978-3-031-92383-8_60" target="_blank" >10.1007/978-3-031-92383-8_60</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Statistical Analysis of Bivariate Densities with Compositional Splines

Popis výsledku v původním jazyce

In general, densities occur naturally as data as a result of massive data aggregation. Thus, their suitable approximation for reliable (functional) data analysis is crucial not only for the univariate case but also for multivariate in general. However, their specific features, i.e. scale invariance and relative scale, have to be taken into account to build a suitable spline basis. This can be achieved using Bayes space methodology, which also allows to decompose densities into their interactive and independent part, which offers a powerful tool for the study of the dependence structure between random variables. Therefore, it is desirable for the spline approximation to admit the same decomposition. In addition, Bayes spaces methodology enables to convert densities to a standard Lebesgue space of square integrable functions using centered log-ratio transformation in order to use standard operations of the Lebesgue space, where, as a consequence, densities fulfill zero integral constraint. We propose a new bivariate spline basis for clr-transformed densities respecting the zero integral constraint. The practical impact of the proposed basis will be demonstrated on a regression model with a functional response for real geochemical data.

Název v anglickém jazyce

Statistical Analysis of Bivariate Densities with Compositional Splines

Popis výsledku anglicky

In general, densities occur naturally as data as a result of massive data aggregation. Thus, their suitable approximation for reliable (functional) data analysis is crucial not only for the univariate case but also for multivariate in general. However, their specific features, i.e. scale invariance and relative scale, have to be taken into account to build a suitable spline basis. This can be achieved using Bayes space methodology, which also allows to decompose densities into their interactive and independent part, which offers a powerful tool for the study of the dependence structure between random variables. Therefore, it is desirable for the spline approximation to admit the same decomposition. In addition, Bayes spaces methodology enables to convert densities to a standard Lebesgue space of square integrable functions using centered log-ratio transformation in order to use standard operations of the Lebesgue space, where, as a consequence, densities fulfill zero integral constraint. We propose a new bivariate spline basis for clr-transformed densities respecting the zero integral constraint. The practical impact of the proposed basis will be demonstrated on a regression model with a functional response for real geochemical data.

Druh

D - Stať ve sborníku

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2025

Kód důvěrnosti údajů

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

Název statě ve sborníku

New Trends in Functional Statistics and Related Fields

ISBN

978-3-031-92382-1

ISSN

1431-1968

e-ISSN

2628-8966

Počet stran výsledku

8

Strana od-do

"503–510"

Název nakladatele

Springer

Místo vydání

Cham

Místo konání akce

Novara, Itálie

Datum konání akce

25. 6. 2024

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

001545850800060