Title of article
Estimation of Non-sharp Support Boundaries
Author/Authors
Hardle، Wolfgang Karl نويسنده , , W. and Park، نويسنده , , B.U. and Tsybakov، نويسنده , , A.B.، نويسنده ,
Issue Information
دوفصلنامه با شماره پیاپی سال 1995
Pages
14
From page
205
To page
218
Abstract
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 R2. 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 γ and that the values of density f decrease to 0 as the power α 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−γ/((α + 1)γ + 1)) within this class of densities.
Journal title
Journal of Multivariate Analysis
Serial Year
1995
Journal title
Journal of Multivariate Analysis
Record number
1557331
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