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On the estimation of the mean density of random closed sets

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  • Camerlenghi, F.
  • Capasso, V.
  • Villa, E.

Abstract

Many real phenomena may be modeled as random closed sets in Rd, of different Hausdorff dimensions. Of particular interest are cases in which their Hausdorff dimension, say n, is strictly less than d, such as fiber processes, boundaries of germ–grain models, and n-facets of random tessellations. A crucial problem is the estimation of pointwise mean densities of absolutely continuous, and spatially inhomogeneous random sets, as defined by the authors in a series of recent papers. While the case n=0 (random vectors, point processes, etc.) has been, and still is, the subject of extensive literature, in this paper we face the general case of any n

Suggested Citation

  • Camerlenghi, F. & Capasso, V. & Villa, E., 2014. "On the estimation of the mean density of random closed sets," Journal of Multivariate Analysis, Elsevier, vol. 125(C), pages 65-88.
    • Handle: RePEc:eee:jmvana:v:125:y:2014:i:c:p:65-88
    DOI: 10.1016/j.jmva.2013.12.003
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    Cited by:

    1. Federico Camerlenghi & Claudio Macci & Elena Villa, 2021. "Asymptotic behavior of mean density estimators based on a single observation: the Boolean model case," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(5), pages 1011-1035, October.

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