Estimating the support of multivariate densities under measurement error

  • Authors:

  • Alexander Meister

  • Affiliations:

  • Centre for Mathematics and its Applications, Mathematical Sciences Institute, Australian National University, Canberra, Australia

  • Venue:
  • Journal of Multivariate Analysis
  • Year:
  • 2006

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Abstract

We consider the problem of estimating the support of a multivariate density based on contaminated data. We introduce an estimator, which achieves consistency under weak conditions on the target density and its support, respecting the assumption of a known error density. Especially, no smoothness or sharpness assumptions are needed for the target density. Furthermore, we derive an iterative and easily computable modification of our estimation and study its rates of convergence in a special case; a numerical simulation is given.