The problem of the evaluation and estimation of the mean density of random closed sets in Rd with integer Hausdorff dimension 0 < n < d, is of great interest in many different scientific and technological fields. Among the estimators of the mean density available in literature, the so-called "Minkowski content"-based estimator reveals its benefits in applications in the non-stationary cases. We introduce here a multivariate version of such estimator, and we study its asymptotical properties by means of large and moderate deviation results. In particular we prove that the estimator is strongly consistent and asymptotically Normal. Furthermore we also provide confidence regions for the mean density of the involved random closed set in m ≥ 1 distinct points x1, …, xm ∈ Rd.

Camerlenghi, F., Macci, C., Villa, E. (2016). Asymptotic results for multivariate estimators of the mean density of random closed sets. ELECTRONIC JOURNAL OF STATISTICS, 10(2), 2066-2096 [10.1214/16-EJS1159].

Asymptotic results for multivariate estimators of the mean density of random closed sets

Camerlenghi, F;
2016

Abstract

The problem of the evaluation and estimation of the mean density of random closed sets in Rd with integer Hausdorff dimension 0 < n < d, is of great interest in many different scientific and technological fields. Among the estimators of the mean density available in literature, the so-called "Minkowski content"-based estimator reveals its benefits in applications in the non-stationary cases. We introduce here a multivariate version of such estimator, and we study its asymptotical properties by means of large and moderate deviation results. In particular we prove that the estimator is strongly consistent and asymptotically Normal. Furthermore we also provide confidence regions for the mean density of the involved random closed set in m ≥ 1 distinct points x1, …, xm ∈ Rd.
Articolo in rivista - Articolo scientifico
Confidence regions; Large deviations; Minkowski content; Moderate deviations; Random closed sets; Statistics and Probability
English
2066
2096
31
Camerlenghi, F., Macci, C., Villa, E. (2016). Asymptotic results for multivariate estimators of the mean density of random closed sets. ELECTRONIC JOURNAL OF STATISTICS, 10(2), 2066-2096 [10.1214/16-EJS1159].
Camerlenghi, F; Macci, C; Villa, E
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/182534
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