Kernel estimators and the Dvoretzky–Kiefer–Wolfowitz inequality

Volume 34 / 2007

Ryszard Zieli/nski Applicationes Mathematicae 34 (2007), 401-404 MSC: 62G20, 62G30, 62G07. DOI: 10.4064/am34-4-3


It turns out that for standard kernel estimators no inequality like that of Dvoretzky–Kiefer–Wolfowitz can be constructed, and as a result it is impossible to answer the question of how many observations are needed to guarantee a prescribed level of accuracy of the estimator. A remedy is to adapt the bandwidth to the sample at hand.


  • Ryszard Zieli/nskiInstitute of Mathematics
    Polish Academy of Sciences
    00-956 Warszawa, Poland

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