Título:
Detection of low dimensionality and data denoising via set estimation techniques
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Autor:
Aaron, Catherine
Cholaquidis, Alejandro
Cuevas, A.
Cholaquidis, Alejandro
Cuevas, A.
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Tipo de documento:
Artículo
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Palabras clave:
Boundary estimation
Denoising procedure
Minkowski content
Denoising procedure
Minkowski content
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Año de publicación:
2017
Contenido:
Resumen:
This work is closely related to the theories of set estimation and manifold estimation. Our object of interest is a, possibly lower-dimensional, compact set S ⊂ ℝd. The general aim is to identify (via stochastic procedures) some qualitative or quantitative features of S, of geometric or topological character. The available information is just a random sample of points drawn on S. The term “to identify” means here to achieve a correct answer almost surely (a.s.) when the sample size tends to infinity. More specifically the paper aims at giving some partial answers to the following questions: is S full dimensional? Is S “close to a lower dimensional set” M? If so, can we estimate M or some functionals of M (in particular, the Minkowski content of M)? As an important auxiliary tool in the answers of these questions, a denoising procedure is proposed in order to partially remove the noise in the original data. The theoretical results are complemented with some simulations and graphical illustrations. © 2017, Institute of Mathematical Statistics.
Descripción:
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Editorial:
Institute of Mathematical Statistics
EN:
Electronic Journal of Statistics, 2017, 11 (2): 4596-4628
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Citación:
Aaron, C.,Cholaquidis, A., Cuevas, A.Detection of low dimensionality and data denoising via set estimation techniques. Electronic Journal of Statistics, 2017, 11 (2): 4596-4628.doi: 10.1214/17-EJS1370
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ISSN:
1935-7524
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Licencia:
Licencia Creative Commons Atribución (CC –BY 4.0)
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| Ficheros | Descripción | Tamaño | Formato | ||
|---|---|---|---|---|---|
| 10121417EJS1370.pdf | — | 7.41 MB | Adobe PDF |