Methods for Estimation of Convex Sets

  title={Methods for Estimation of Convex Sets},
  author={Victor-Emmanuel Brunel},
  journal={Statistical Science},
In the framework of shape constrained estimation, we review methods and works done in convex set estimation. Some methods are standard in statistics, coming especially from the theory of empirical processes, but we more geometric methods that are specific to convex set estimation. The statistical problems that we review include density support estimation, estimation of the level sets of densities or depth functions, nonparametric regression, etc. We focus on the estimation of convex sets under… 
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