Testing Equality of Distributions of Random Convex Compact Sets via Theory of n-Distances

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F21%3A00355035" target="_blank" >RIV/68407700:21230/21:00355035 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1007/s11009-019-09747-z" target="_blank" >https://doi.org/10.1007/s11009-019-09747-z</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s11009-019-09747-z" target="_blank" >10.1007/s11009-019-09747-z</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Testing Equality of Distributions of Random Convex Compact Sets via Theory of n-Distances

Popis výsledku v původním jazyce

This paper concerns a method of testing the equality of distributions of random convex compact sets. The main theoretical result involves a construction of a metric on the space of distributions of random convex compact sets. We obtain it by using the theory of n-distances and the redefined characteristic function of random convex compact set. We propose an approximation of the metric through its finite-dimensional counterparts. This result leads to a new statistical test for testing the equality of distributions of two random convex compact sets. Consequently, we show a heuristic approach how to determine whether two realisations of random sets that can be approximated by a union of identically distributed random convex compact sets come from the same underlying process using the constructed test. Each procedure is justified by an extensive simulation study and the heuristic method for comparing random sets using their convex compact counterparts is moreover applied to real data concerning histological images of two different types of mammary tissue.

Název v anglickém jazyce

Testing Equality of Distributions of Random Convex Compact Sets via Theory of n-Distances

Popis výsledku anglicky

This paper concerns a method of testing the equality of distributions of random convex compact sets. The main theoretical result involves a construction of a metric on the space of distributions of random convex compact sets. We obtain it by using the theory of n-distances and the redefined characteristic function of random convex compact set. We propose an approximation of the metric through its finite-dimensional counterparts. This result leads to a new statistical test for testing the equality of distributions of two random convex compact sets. Consequently, we show a heuristic approach how to determine whether two realisations of random sets that can be approximated by a union of identically distributed random convex compact sets come from the same underlying process using the constructed test. Each procedure is justified by an extensive simulation study and the heuristic method for comparing random sets using their convex compact counterparts is moreover applied to real data concerning histological images of two different types of mammary tissue.

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/GA19-04412S" target="_blank" >GA19-04412S: Nové přístupy k modelování a statistice náhodných množin</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

METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY

ISSN

1387-5841

e-ISSN

1573-7713

Svazek periodika

23

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

24

Strana od-do

503-526

Kód UT WoS článku

000495963200001

EID výsledku v databázi Scopus

2-s2.0-85075210515