Polynomial volume estimation and its applications
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Título: | Polynomial volume estimation and its applications |
Autor/a: | Cuevas González, Antonio Pateiro López, Beatriz |
Centro/Departamento: | Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización |
Palabras chave: | Set estimation | Volume estimation | Boundary length estimation | |
Data: | 2018 |
Editor: | Elsevier |
Cita bibliográfica: | Antonio Cuevas, Beatriz Pateiro-López (2018) Polynomial volume estimation and its applications, Journal of Statistical Planning and Inference, Volume 196, pp 174-184, DOI: 10.1016/j.jspi.2017.11.005 |
Resumo: | Given a compact set S ⊂ R d we consider the problem of estimating, from a random sample of points, the Lebesgue measure of S, µ(S), and its boundary measure, L(S) (as defined by the Minkowski content of ∂S). This topic has received some attention, especially in the two-dimensional case d = 2, motivated by applications in image analysis. A new method to simultaneously estimate µ(S) and L(S) from a sample of points inside S is proposed. The basic idea is to assume that S has a polynomial volume, that is, that V (r) := µ{x : d(x, S) ≤ r} is a polynomial in r of degree d, for all r in some interval [0, R). We develop a minimum distance approach to estimate the coefficients of V (r) and, in particular µ(S) and L(S), which correspond, respectively, to the independent term and the first degree coefficient of V (r). The strong consistency of the proposed estimators is proved. Some numerical illustrations are given |
Versión do editor: | https://doi.org/10.1016/j.jspi.2017.11.005 |
URI: | http://hdl.handle.net/10347/18631 |
DOI: | 10.1016/j.jspi.2017.11.005 |
ISSN: | 0378-3758 |
Dereitos: | © 2017 Elsevier B.V. All Rights reserved. This manuscript version is made available under the CC-BY-NC-ND 4.0 license (http://creativecommons.org/licenses/by-ncnd/4.0/) Attribution-NonCommercial-NoDerivatives 4.0 Internacional |
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