Two-step estimation procedures for inhomogeneous shot-noise Cox processes

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F17%3A10365532" target="_blank" >RIV/00216208:11320/17:10365532 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1007/s10463-016-0556-y" target="_blank" >http://dx.doi.org/10.1007/s10463-016-0556-y</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10463-016-0556-y" target="_blank" >10.1007/s10463-016-0556-y</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Two-step estimation procedures for inhomogeneous shot-noise Cox processes

Popis výsledku v původním jazyce

In the present paper, we discuss and compare several two-step estimation procedures for inhomogeneous shot-noise Cox processes. The intensity function is parametrized by the inhomogeneity parameters while the pair-correlation function is parametrized by the interaction parameters. The suggested procedures are based on a combination of Poisson likelihood estimation of the inhomogeneity parameters in the first step and an adaptation of a method from the homogeneous case for estimation of the interaction parameters in the second step. The adapted methods, based on minimum contrast estimation, composite likelihood and Palm likelihood, are compared both theoretically and by means of a simulation study. The general conclusion from the simulation study is that the three estimation methods have similar performance. Two-step estimation with Palm likelihood has not been considered before and is motivated by the superior performance of the Palm likelihood in the stationary case for estimation of certain parameters of interest. Asymptotic normality of the two-step estimator with Palm likelihood is proved.

Název v anglickém jazyce

Two-step estimation procedures for inhomogeneous shot-noise Cox processes

Popis výsledku anglicky

In the present paper, we discuss and compare several two-step estimation procedures for inhomogeneous shot-noise Cox processes. The intensity function is parametrized by the inhomogeneity parameters while the pair-correlation function is parametrized by the interaction parameters. The suggested procedures are based on a combination of Poisson likelihood estimation of the inhomogeneity parameters in the first step and an adaptation of a method from the homogeneous case for estimation of the interaction parameters in the second step. The adapted methods, based on minimum contrast estimation, composite likelihood and Palm likelihood, are compared both theoretically and by means of a simulation study. The general conclusion from the simulation study is that the three estimation methods have similar performance. Two-step estimation with Palm likelihood has not been considered before and is motivated by the superior performance of the Palm likelihood in the stationary case for estimation of certain parameters of interest. Asymptotic normality of the two-step estimator with Palm likelihood is proved.

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/GAP201%2F10%2F0472" target="_blank" >GAP201/10/0472: Stochastická geometrie - nehomogenita, kótování, dynamika a stereologie</a><br>

Návaznosti

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

Rok uplatnění

2017

Kód důvěrnosti údajů

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

Název periodika

Annals of the Institute of Statistical Mathematics

ISSN

0020-3157

e-ISSN

—

Svazek periodika

69

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

30

Strana od-do

513-542

Kód UT WoS článku

000399700600002

EID výsledku v databázi Scopus

2-s2.0-84975678749