Estimation of Non-sharp Support Boundaries
Let X1, ..., Xn be independent identically distributed observations from an unknown probability density f(·), such that its support G = supp f is a subset of the unit square in 2. We consider the problem of estimating G from the sample X1, ..., Xn, under the assumption that the boundary of G is a function of smoothness [gamma] and that the values of density f decrease to 0 as the power [alpha] of the distance from the boundary. We show that a certain piecewise-polynomial estimator of G has optimal rate of convergence (namely, the rate n-[gamma]/(([alpha] + 1)[gamma] + 1)) within this class of densities.
Year of publication: |
1995
|
---|---|
Authors: | Hardle, W. ; Park, B. U. ; Tsybakov, A. B. |
Published in: |
Journal of Multivariate Analysis. - Elsevier, ISSN 0047-259X. - Vol. 55.1995, 2, p. 205-218
|
Publisher: |
Elsevier |
Saved in:
Online Resource
Saved in favorites
Similar items by person
-
Hardle, W., (1995)
-
Estimation of support of a probability density and estimation of support functionals
Korostelev, Aleksandr P., (1992)
-
Minimax linewise algorithm for image reconstruction
Korostelev, Aleksandr P., (1992)
- More ...