Weighting the domain of probability densities in functional data analysis

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F20%3A73604821" target="_blank" >RIV/61989592:15310/20:73604821 - isvavai.cz</a>

Result on the web

<a href="https://obd.upol.cz/id_publ/333184707" target="_blank" >https://obd.upol.cz/id_publ/333184707</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1002/sta4.283" target="_blank" >10.1002/sta4.283</a>

Result language

angličtina

Original language name

Weighting the domain of probability densities in functional data analysis

Original language description

In functional data analysis, some regions of the domain of the functions can be of more interest than others owing to the quality of measurement, relative scale of the domain, or simply some external reason (e.g. interest of stakeholders). Weighting the domain is of interest particularly with probability density functions (PDFs), as derived from distributional data, which often aggregate measurements of different quality or are affected by scale effects. A weighting scheme can be embedded into the underlying sample space of a PDF when it is considered as continuous compositions applying the theory of Bayes spaces. The origin of a Bayes space is determined by a given reference measure, and this can be easily changed through the well-known chain rule. This work provides a formal framework for defining weights through a reference measure, and it is used to develop a weighting scheme on the bounded domain of distributional data. The impact on statistical analysis is illustrated through an application to functional principal component analysis of income distribution data. Moreover, a novel centred log-ratio transformation is proposed to map a weighted Bayes space into an unweighted L2 space, enabling to use most tools developed in functional data analysis (e.g. clustering and regression analysis) while accounting for the weighting scheme. The potential of our proposal is shown on a real case study using Italian income data.

Czech name

—

Czech description

—

Type

J_SC - Article in a specialist periodical, which is included in the SCOPUS database

CEP classification

—

OECD FORD branch

10103 - Statistics and probability

Project

<a href="/en/project/GA19-01768S" target="_blank" >GA19-01768S: Separation of geochemical signals in sediments: application of advanced statistical methods on large geochemical datasets</a><br>

Continuities

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

Publication year

2020

Confidentiality

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

Name of the periodical

Stat

ISSN

2049-1573

e-ISSN

—

Volume of the periodical

9

Issue of the periodical within the volume

1

Country of publishing house

US - UNITED STATES

Number of pages

13

Pages from-to

"e283-1"-"e283-13"

UT code for WoS article

000614806100027

EID of the result in the Scopus database

2-s2.0-85094180322