The asymptotic properties of maximum likelihood estimators of marked Poisson processes with a cyclic intensity measure
type: Item
instance of: scholarly article
title: The asymptotic properties of maximum likelihood estimators of marked Poisson processes with a cyclic intensity measure
zbMATH Open document ID: 0629.62089
DOI: 10.1007/BF02613141
author: B. George
published in: Metrika
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/176111
review text: Let \(\theta\) and \(\gamma\) be vector parameters and \((\tau_ n,\xi_ n)_ N\) be a marked point Poisson process with periodic occurrence intensity \(\lambda\) (t;\(\theta)\) and conditional density h(x;t,\(\gamma)\) of i.i.d. events \(\xi_ n\), given \(\tau_ n\). The strong consistency, asymptotic normality and efficiency of MLE for (\(\theta\),\(\gamma)\) by \(T\to \infty\) are established under exponential parametric form of \(\lambda\). Results of this kind were known only in the case of a simple Poisson process. An application to a hydrological flood peaks model is suggested.
Mathematics Subject Classification ID: 62M09
Mathematics Subject Classification ID: 62F12
Mathematics Subject Classification ID: 62E20
zbMATH DE Number: 4024571
zbMATH Keywords: large sample behavior
zbMATH Keywords: hydrology
zbMATH Keywords: asymptotic efficiency
zbMATH Keywords: asymptotic distribution
zbMATH Keywords: marked point Poisson process
zbMATH Keywords: periodic occurrence intensity
zbMATH Keywords: conditional density
zbMATH Keywords: strong consistency
zbMATH Keywords: asymptotic normality
zbMATH Keywords: exponential parametric form
zbMATH Keywords: hydrological flood peaks model
MaRDI profile type: Publication
cites work: Q3336492
cites work: Q3051273
cites work: Two extreme value processes arising in hydrology
cites work: Q4048357
cites work: Q5613624
cites work: Extreme value processes and the evaluation of risk in flood analysis
cites work: Q3965448
cites work: Remarks on the theory, computation and application of the spectral analysis of series of events
cites work: The asymptotic behaviour of maximum likelihood estimators for stationary point processes
description: scientific article; zbMATH DE number 4024571