The asymptotic properties of maximum likelihood estimators of marked Poisson processes with a cyclic intensity measure
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.
scientific article; zbMATH DE number 4024571