Estimating the support of multivariate densities under measurement error
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.
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Volume (Year): 97 (2006)
Issue (Month): 8 (September)
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References listed on IDEAS
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- Hall, Peter & Nussbaum, Michael & Stern, Steven E., 1997. "On the Estimation of a Support Curve of Indeterminate Sharpness," Journal of Multivariate Analysis, Elsevier, vol. 62(2), pages 204-232, August.
- Hall, P. & Simar, L., 2000.
"Estimating a Changepoint, Boundary of Frontier in the Presence of Observation Error,"
0012, Catholique de Louvain - Institut de statistique.
- Hall P. & Simar L., 2002. "Estimating a Changepoint, Boundary, or Frontier in the Presence of Observation Error," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 523-534, June.
- Goldenshluger, A. & Tsybakov, A., 2004. "Estimating the endpoint of a distribution in the presence of additive observation errors," Statistics & Probability Letters, Elsevier, vol. 68(1), pages 39-49, June.
- Hardle, W. & Park, B. U. & Tsybakov, A. B., 1995. "Estimation of Non-sharp Support Boundaries," Journal of Multivariate Analysis, Elsevier, vol. 55(2), pages 205-218, November.
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