• 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