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Uniform and individual convergence rates for convex density classes

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  • Meister Alexander

Abstract

In this paper, we prove coincidence of uniform and individual convergence rates for convex density classes, which are Baire spaces with respect to the L1(Rd)-metric, in the field of nonparametric estimation. We show that for convex density classes, which are no Baire spaces, the validity of this result is not guaranteed, in general.

Suggested Citation

  • Meister Alexander, 2008. "Uniform and individual convergence rates for convex density classes," Statistics & Risk Modeling, De Gruyter, vol. 26(1), pages 25-34, March.
    • Handle: RePEc:bpj:strimo:v:26:y:2008:i:1:p:25-34:n:3
    DOI: 10.1524/stnd.2008.0910
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    References listed on IDEAS

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    1. Devroye, Luc, 1995. "Another proof of a slow convergence result of Birgé," Statistics & Probability Letters, Elsevier, vol. 23(1), pages 63-67, April.
    2. Andras Antos & Gábor Lugosi, 1997. "Strong minimax lower bounds for learning," Economics Working Papers 197, Department of Economics and Business, Universitat Pompeu Fabra.
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    1. Beirlant, Jan & Devroye, Luc, 1999. "On the impossibility of estimating densities in the extreme tail," Statistics & Probability Letters, Elsevier, vol. 43(1), pages 57-64, May.

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