Asymptotic behavior of mean density estimators based on a single observation: the Boolean model case

The mean density estimation of a random closed set in ℝ^d , 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更多