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

Federico Camerlenghi (), Claudio Macci () and Elena Villa ()
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Federico Camerlenghi: Università di Milano - Bicocca
Claudio Macci: Università di Roma Tor Vergata
Elena Villa: Università degli Studi di Milano

Annals of the Institute of Statistical Mathematics, 2021, vol. 73, issue 5, No 6, 1035 pages

Abstract: Abstract The mean density estimation of a random closed set in $$\mathbb {R}^d$$ 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 $$\Theta _n$$ Θ n belongs to the quite general class of stationary Boolean models with Hausdorff dimension $$n

Keywords: Hausdorff measure; Large deviations; Moderate deviations; Point processes; Stochastic geometry (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10463-020-00775-y

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