Compositional splines for representation of density functions

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F21%3A73603147" target="_blank" >RIV/61989592:15310/21:73603147 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/61989592:15510/21:73603147

Výsledek na webu

<a href="https://link.springer.com/content/pdf/10.1007/s00180-020-01042-7.pdf" target="_blank" >https://link.springer.com/content/pdf/10.1007/s00180-020-01042-7.pdf</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00180-020-01042-7" target="_blank" >10.1007/s00180-020-01042-7</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Compositional splines for representation of density functions

Popis výsledku v původním jazyce

In the context of functional data analysis, probability density functions as non-negative functions are characterized by specific properties of scale invariance and relative scale which enable to represent them with the unit integral constraint without loss of information. On the other hand, all these properties are a challenge when the densities need to be approximated with spline functions, including construction of the respective spline basis. The Bayes space methodology of density functions enables to express them as real functions in the standard L-2 space using the centered log-ratio transformation. The resulting functions satisfy the zero integral constraint. This is a key to propose a new spline basis, holding the same property, and consequently to build a new class of spline functions, called compositional splines, which can approximate probability density functions in a consistent way. The paper provides also construction of smoothing compositional splines and possible orthonormalization of the spline basis which might be useful in some applications. Finally, statistical processing of densities using the new approximation tool is demonstrated in case of simplicial functional principal component analysis with anthropometric data.

Název v anglickém jazyce

Compositional splines for representation of density functions

Popis výsledku anglicky

In the context of functional data analysis, probability density functions as non-negative functions are characterized by specific properties of scale invariance and relative scale which enable to represent them with the unit integral constraint without loss of information. On the other hand, all these properties are a challenge when the densities need to be approximated with spline functions, including construction of the respective spline basis. The Bayes space methodology of density functions enables to express them as real functions in the standard L-2 space using the centered log-ratio transformation. The resulting functions satisfy the zero integral constraint. This is a key to propose a new spline basis, holding the same property, and consequently to build a new class of spline functions, called compositional splines, which can approximate probability density functions in a consistent way. The paper provides also construction of smoothing compositional splines and possible orthonormalization of the spline basis which might be useful in some applications. Finally, statistical processing of densities using the new approximation tool is demonstrated in case of simplicial functional principal component analysis with anthropometric data.

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/GA19-01768S" target="_blank" >GA19-01768S: Separace geochemických signálů v sedimentech: aplikace pokročilých statistických metod na rozsáhlé geochemické datové soubory</a><br>

Návaznosti

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

Rok uplatnění

2021

Kód důvěrnosti údajů

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

Název periodika

COMPUTATIONAL STATISTICS

ISSN

0943-4062

e-ISSN

—

Svazek periodika

36

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

34

Strana od-do

1031-1064

Kód UT WoS článku

000579680800002

EID výsledku v databázi Scopus

2-s2.0-85092765869