Estimation of Non-sharp Support Boundaries
Let X1, ..., Xn be independent identically distributed observations from an unknown probability density f(Â·), 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.
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Volume (Year): 55 (1995)
Issue (Month): 2 (November)
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