Free Access
Volume 20, 2016
Page(s) 332 - 348
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]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.