NUMERICAL EXPERIMENTS FOR THE ESTIMATION OF MEAN DENSITIES OF RANDOM SETS

• Main Authors: Federico Camerlenghi, Vincenzo Capasso, Elena Villa
• Format: Article
• Language: English
• Published: Slovenian Society for Stereology and Quantitative Image Analysis 2014-05-01
• Series: Image Analysis and Stereology
• Subjects: density estimator; Hausdorff dimension; Hausdorff measure; kernel estimate; Minkowski content; random closed set; stochastic geometry
• Online Access: http://www.ias-iss.org/ojs/IAS/article/view/1089

Many real phenomena may be modelled as random closed sets in <span>ℝ</span>^d, of different Hausdorff dimensions. The problem of the estimation of pointwise mean densities of absolutely continuous, and spatially inhomogeneous, random sets with Hausdorff dimension <em>n</em> &lt; <em>d</em>, has been the subject of extended mathematical analysis by the authors. In particular, two different kinds of estimators have been recently proposed, the first one is based on the notion of Minkowski content, the second one is a kernel-type estimator generalizing the well-known kernel density estimator for random variables. The specific aim of the present paper is to validate the theoretical results on statistical properties of those estimators by numerical experiments. We provide a set of simulations which illustrates their valuable properties via typical examples of lower dimensional random sets.