Estimators of the asymptotic variance of stationary point processes - a comparison

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F11%3A10099287" target="_blank" >RIV/00216208:11320/11:10099287 - isvavai.cz</a>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Estimators of the asymptotic variance of stationary point processes - a comparison

Popis výsledku v původním jazyce

We investigate estimators of the asymptotic variance of a d-dimensional stationary point process which can be observed in convex and compact sampling window. Asymptotic variance is defined by asymptotic relation and its existence is guaranteed whenever the corresponding reduced covariance measure has finite total variation. The three estimators discussed in the paper are the kernel estimator, the estimator based on the second order intesity of the point process and the subsampling estimator. We study the mean square consistency of the estimators. Since the expressions for the variance of the estimators are not available in closed form and depend on higher order moment measures of the point process, only the bias of the estimators can be compared theoretically. The second part of the paper is therefore devoted to a simulation study which compares the efficiency of the estimators by means of the mean squared error and for several clustered and repulsive point processes observed on middle

Název v anglickém jazyce

Estimators of the asymptotic variance of stationary point processes - a comparison

Popis výsledku anglicky

We investigate estimators of the asymptotic variance of a d-dimensional stationary point process which can be observed in convex and compact sampling window. Asymptotic variance is defined by asymptotic relation and its existence is guaranteed whenever the corresponding reduced covariance measure has finite total variation. The three estimators discussed in the paper are the kernel estimator, the estimator based on the second order intesity of the point process and the subsampling estimator. We study the mean square consistency of the estimators. Since the expressions for the variance of the estimators are not available in closed form and depend on higher order moment measures of the point process, only the bias of the estimators can be compared theoretically. The second part of the paper is therefore devoted to a simulation study which compares the efficiency of the estimators by means of the mean squared error and for several clustered and repulsive point processes observed on middle

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/GP201%2F08%2FP100" target="_blank" >GP201/08/P100: Modelování a statistika prostorových Coxových bodových procesů</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2011

Kód důvěrnosti údajů

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

Název periodika

Kybernetika

ISSN

0023-5954

e-ISSN

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Svazek periodika

47

Číslo periodika v rámci svazku

5

Stát vydavatele periodika

CZ - Česká republika

Počet stran výsledku

18

Strana od-do

678-695

Kód UT WoS článku

000297954400002

EID výsledku v databázi Scopus

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