The mean density estimation of a random closed set in Rd, based on a single observation, is a crucial problem in several application areas. In the case of stationary random sets, a common practice to estimate the mean density is to take the n-dimensional volume fraction with observation window as large as possible. In the present paper, we provide large and moderate deviation results for these estimators when the random closed set Θ n belongs to the quite general class of stationary Boolean models with Hausdorff dimension n< d. Moreover, we establish a central limit theorem and a Berry–Esseen bound for the family of estimators under study. Our findings allow to recover some well-known results in the literature on Boolean models. Finally, we also provide a guideline for the estimation of the mean density of non-stationary Boolean models characterized by high intensity of the underlying Poisson point process.
Camerlenghi, F., Macci, C., & Villa, E. (2021). Asymptotic behavior of mean density estimators based on a single observation: the Boolean model case. ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS.
|Citazione:||Camerlenghi, F., Macci, C., & Villa, E. (2021). Asymptotic behavior of mean density estimators based on a single observation: the Boolean model case. ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS.|
|Tipo:||Articolo in rivista - Articolo scientifico|
|Carattere della pubblicazione:||Scientifica|
|Presenza di un coautore afferente ad Istituzioni straniere:||No|
|Titolo:||Asymptotic behavior of mean density estimators based on a single observation: the Boolean model case|
|Autori:||Camerlenghi, F; Macci, C; Villa, E|
CAMERLENGHI, FEDERICO (Corresponding)
|Data di pubblicazione:||2021|
|Rivista:||ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.1007/s10463-020-00775-y|
|Appare nelle tipologie:||01 - Articolo su rivista|