NUMERICAL EXPERIMENTS FOR THE ESTIMATION OF MEAN DENSITIES OF RANDOM SETS
Many real phenomena may be modelled as random closed sets in <span>ℝ</span><sup>d</sup>, of different Hausdorff dimensions. The problem of the estimation of pointwise mean densities of absolutely continuous, and spatially inhomogeneous, random sets with Hausdorff dimension &l...
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| Format: | Article |
| Language: | English |
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Slovenian Society for Stereology and Quantitative Image Analysis
2014-05-01
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| Series: | Image Analysis and Stereology |
| Subjects: | |
| Online Access: | http://www.ias-iss.org/ojs/IAS/article/view/1089 |
| _version_ | 1828843426717630464 |
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| author | Federico Camerlenghi Vincenzo Capasso Elena Villa |
| author_facet | Federico Camerlenghi Vincenzo Capasso Elena Villa |
| author_sort | Federico Camerlenghi |
| collection | DOAJ |
| description | Many real phenomena may be modelled as random closed sets in <span>ℝ</span><sup>d</sup>, 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> < <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. |
| first_indexed | 2024-12-12T20:45:00Z |
| format | Article |
| id | doaj.art-6d32769d08bd4a6185478a683a49780c |
| institution | Directory Open Access Journal |
| issn | 1580-3139 1854-5165 |
| language | English |
| last_indexed | 2024-12-12T20:45:00Z |
| publishDate | 2014-05-01 |
| publisher | Slovenian Society for Stereology and Quantitative Image Analysis |
| record_format | Article |
| series | Image Analysis and Stereology |
| spelling | doaj.art-6d32769d08bd4a6185478a683a49780c2022-12-22T00:12:36ZengSlovenian Society for Stereology and Quantitative Image AnalysisImage Analysis and Stereology1580-31391854-51652014-05-01332839410.5566/ias.v33.p83-94913NUMERICAL EXPERIMENTS FOR THE ESTIMATION OF MEAN DENSITIES OF RANDOM SETSFederico Camerlenghi0Vincenzo Capasso1Elena Villa2Dept. of Mathematics, Universita' degli Studi di PaviaDept. of Mathematics, Universita' degli Studi di MilanoDept. of Mathematics, Universita' degli Studi di MilanoMany real phenomena may be modelled as random closed sets in <span>ℝ</span><sup>d</sup>, 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> < <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.http://www.ias-iss.org/ojs/IAS/article/view/1089density estimatorHausdorff dimensionHausdorff measurekernel estimateMinkowski contentrandom closed setstochastic geometry |
| spellingShingle | Federico Camerlenghi Vincenzo Capasso Elena Villa NUMERICAL EXPERIMENTS FOR THE ESTIMATION OF MEAN DENSITIES OF RANDOM SETS Image Analysis and Stereology density estimator Hausdorff dimension Hausdorff measure kernel estimate Minkowski content random closed set stochastic geometry |
| title | NUMERICAL EXPERIMENTS FOR THE ESTIMATION OF MEAN DENSITIES OF RANDOM SETS |
| title_full | NUMERICAL EXPERIMENTS FOR THE ESTIMATION OF MEAN DENSITIES OF RANDOM SETS |
| title_fullStr | NUMERICAL EXPERIMENTS FOR THE ESTIMATION OF MEAN DENSITIES OF RANDOM SETS |
| title_full_unstemmed | NUMERICAL EXPERIMENTS FOR THE ESTIMATION OF MEAN DENSITIES OF RANDOM SETS |
| title_short | NUMERICAL EXPERIMENTS FOR THE ESTIMATION OF MEAN DENSITIES OF RANDOM SETS |
| title_sort | numerical experiments for the estimation of mean densities of random sets |
| topic | density estimator Hausdorff dimension Hausdorff measure kernel estimate Minkowski content random closed set stochastic geometry |
| url | http://www.ias-iss.org/ojs/IAS/article/view/1089 |
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