Estimation of the Location of a 0-type or $\infty$-type Singularity by Poisson Observations
| dc.creator | Dachian, Serguei | |
| dc.date | 2006-11-02 | |
| dc.date.accessioned | 2026-07-07T08:08:18Z | |
| dc.date.available | 2026-07-07T08:08:18Z | |
| dc.description | We consider an inhomogeneous Poisson process $X$ on $[0,T]$. The intensity function of $X$ is supposed to be strictly positive and smooth on $[0,T]$ except at the point $θ$, in which it has either a 0-type singularity (tends to 0 like $\abs{x}^p$, $p\in(0,1)$), or an $\infty$-type singularity (tends to $\infty$ like $\abs{x}^p$, $p\in(-1,0)$). We suppose that we know the shape of the intensity function, but not the location of the singularity. We consider the problem of estimation of this location (shift) parameter $θ$ based on $n$ observations of the process $X$. We study the Bayesian estimators and, in the case $p>0$, the maximum likelihood estimator. We show that these estimators are consistent, their rate of convergence is $n^{1/(p+1)}$, they have different limit distributions, and the Bayesian estimators are asymptotically efficient. | |
| dc.identifier | https://arxiv.org/abs/math/0611043 | |
| dc.identifier | http://arxiv.org/abs/math/0611043 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/131219 | |
| dc.subject | Statistics Theory | |
| dc.subject | 62M05 | |
| dc.title | Estimation of the Location of a 0-type or $\infty$-type Singularity by Poisson Observations | |
| dc.type | text |