Estimation of the Intensity Parameter of the Germ-Grain Quermass-Interaction Model when the Number of Germs is not Observed

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F14%3A00222636" target="_blank" >RIV/68407700:21230/14:00222636 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1111/sjos.12064" target="_blank" >http://dx.doi.org/10.1111/sjos.12064</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1111/sjos.12064" target="_blank" >10.1111/sjos.12064</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Estimation of the Intensity Parameter of the Germ-Grain Quermass-Interaction Model when the Number of Germs is not Observed

Popis výsledku v původním jazyce

The Quermass-interaction model allows to generalize the classical germ-grain Boolean model in adding a morphological interaction between the grains. It enables to model random structures with specific morphologies, which are unlikely to be generated froma Boolean model. The Quermass-interaction model depends in particular on an intensity parameter, which is impossible to estimate from classical likelihood or pseudo-likelihood approaches because the number of points is not observable from a germ-grain set. In this paper, we present a procedure based on the Takacs?Fiksel method, which is able to estimate all parameters of the Quermass-interaction model, including the intensity. An intensive simulation study is conducted to assess the efficiency of the procedure and to provide practical recommendations. It also illustrates that the estimation of the intensity parameter is crucial in order to identify the model. The Quermass-interaction model is finally fitted by our method to P. Diggle?s

Název v anglickém jazyce

Estimation of the Intensity Parameter of the Germ-Grain Quermass-Interaction Model when the Number of Germs is not Observed

Popis výsledku anglicky

The Quermass-interaction model allows to generalize the classical germ-grain Boolean model in adding a morphological interaction between the grains. It enables to model random structures with specific morphologies, which are unlikely to be generated froma Boolean model. The Quermass-interaction model depends in particular on an intensity parameter, which is impossible to estimate from classical likelihood or pseudo-likelihood approaches because the number of points is not observable from a germ-grain set. In this paper, we present a procedure based on the Takacs?Fiksel method, which is able to estimate all parameters of the Quermass-interaction model, including the intensity. An intensive simulation study is conducted to assess the efficiency of the procedure and to provide practical recommendations. It also illustrates that the estimation of the intensity parameter is crucial in order to identify the model. The Quermass-interaction model is finally fitted by our method to P. Diggle?s

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/GP13-05466P" target="_blank" >GP13-05466P: Stochastické modelování a statistická analýza náhodných množin</a><br>

Návaznosti

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

Rok uplatnění

2014

Kód důvěrnosti údajů

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

Název periodika

Scandinavian Journal of Statistics

ISSN

0303-6898

e-ISSN

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Svazek periodika

41

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

21

Strana od-do

809-829

Kód UT WoS článku

000340493800014

EID výsledku v databázi Scopus

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