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All issues Volume 20 (2016) ESAIM: PS, 20 (2016) 332-348 References
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Issue
ESAIM: PS
Volume 20, 2016
Page(s) 332 - 348
DOI https://doi.org/10.1051/ps/2016015
Published online 23 September 2016
  1. C. Aaron, A. Cholaquidis and R. Fraiman, On the maximal multivariate spacing extension and convexity tests. Preprint arXiv:1411.2482 (2014). [Google Scholar]
  2. E. Arias-Castro and A. Rodríguez-Casal, On estimating the perimeter using the alpha-shape. Preprint arXiv:1507.00065 (2015). [Google Scholar]
  3. A. Baíllo and A. Cuevas, On the estimation of a star-shaped set. Adv. Appl. Probab. 33 (2001) 717–726. [CrossRef] [Google Scholar]
  4. A. Baíllo and A. Cuevas, Parametric versus nonparametric tolerance regions in detection problems. Comput. Stat. 21 (2006) 527–536. [Google Scholar]
  5. A. Baíllo, A. Cuevas and A. Justel, Set estimation and nonparametric detection. Can. J. Stat. 28 (2000) 765–782. [CrossRef] [Google Scholar]
  6. J.R. Berrendero, A. Cuevas and B. Pateiro-López, A multivariate uniformity test for the case of unknown support. Stat. Comput. 22 (2012) 259–271. [CrossRef] [Google Scholar]
  7. J. Chevalier, Estimation du support et du contour du support d’une loi de probabilité. Ann. Inst. Henri Poincaré, Probab. Stat. 12 (1976) 339–364. [Google Scholar]
  8. A. Cholaquidis, A. Cuevas and R. Fraiman, On Poincaré cone property. Ann. Stat. 42 (2014) 255–284. [CrossRef] [Google Scholar]
  9. A. Cuevas, On pattern analysis in the non-convex case. Kybernetes 19 (1990) 26–33. [CrossRef] [MathSciNet] [Google Scholar]
  10. A. Cuevas, R. Fraiman and B. Pateiro-López, On statistical properties of sets fulfilling rolling-type conditions. Adv. Appl. Probab. 44 (2012) 311–329. [CrossRef] [Google Scholar]
  11. A. Cuevas and A. Rodríguez-Casal, On boundary estimation. Adv. Appl. Probab. 36 (2004) 340–354. [CrossRef] [Google Scholar]
  12. L. Devroye and G.L. Wise, Detection of abnormal behavior via nonparametric estimation of the support. SIAM J. Appl. Math. 38 (1980) 480–488. [CrossRef] [MathSciNet] [Google Scholar]
  13. L. Dümbgen and G. Walther, Rates of convergence for random approximations of convex sets. Adv. Appl. Probab. 28 (1996) 384–393. [CrossRef] [Google Scholar]
  14. H. Edelsbrunner, Alpha shapes – a survey. To apprear in Tessellations in the Sciences. Springer (2016). [Google Scholar]
  15. C.R. Genovese, M. Perone-Pacifico, I. Verdinelli and L. Wasserman, The geometry of nonparametric filament estimation. J. Amer. Statist. Assoc. 107 (2012) 788–799. [CrossRef] [MathSciNet] [Google Scholar]
  16. U. Grenander, Abstract Inference. Wiley, New York (1981). [Google Scholar]
  17. S. Janson, Maximal spacings in several dimensions. Ann. Probab. 15 (1987) 274–280. [CrossRef] [Google Scholar]
  18. A.P. Korostelëv and A.B. Tsybakov, Minimax Theory of Image Reconstruction. Springer (1993). [Google Scholar]
  19. D.P. Mandal and C.A. Murthy, Selection of alpha for alpha-hull in R2. Pattern Recogn. 30 (1997) 1759–1767. [CrossRef] [Google Scholar]
  20. B. Pateiro-López and A. Rodríguez-Casal, Generalizing the convex hull of a sample: the R package alphahull. J. Stat. Softw. 34 (2010) 1–28. [Google Scholar]
  21. B. Pateiro-López and A. Rodríguez-Casal, Recovering the shape of a point cloud in the plane. TEST 22 (2013) 19–45. [CrossRef] [MathSciNet] [Google Scholar]
  22. M. Reitzner, Random polytopes and the efron’stein jackknife inequality. Ann. Probab. 31 (2003) 2136–2166. [CrossRef] [Google Scholar]
  23. B.D. Ripley and J.P. Rasson, Finding the edge of a poisson forest. J. Appl. Probab. 14 (1977) 483–491. [Google Scholar]
  24. A. Rodríguez-Casal, Set estimation under convexity type assumptions. Ann. Inst. Henri Poincaré, Probab. Stat. 43 (2007) 763–774. [CrossRef] [Google Scholar]
  25. R. Schneider, Random approximation of convex sets. J. Microsc. 151 (1988) 211–227. [CrossRef] [Google Scholar]
  26. R. Schneider, Convex Bodies: the Brunn–Minkowski Theory. Cambridge University Press (1993). [Google Scholar]
  27. J. Serra, Image Analysis and Mathematical Morphology. Academic Press, London (1982). [Google Scholar]
  28. G. Walther, Granulometric smoothing. Ann. Stat. 25 (1997) 2273–2299. [CrossRef] [Google Scholar]
  29. G. Walther, On a generalization of blaschke’s rolling theorem and the smoothing of surfaces. Math. Methods Appl. Sci. 22 (1999) 301–316. [CrossRef] [Google Scholar]

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