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OnLp-convergence rates for statistical functions with application toL-estimates

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Summary

A parameter which may be represented as a functionalT(F) of a distribution functionF may be estimated by the “statistical function”T(Fn), whereFn is the empirical distribution function. Recently, Boos and Serfling (1979, Florida State University Statistics Report No. M 499) obtained sufficient conditions for the Berry-Esseen theorem to hold forT(Fn)-T(F) and applied the results to derive rates of convergence inL∞ forL-estimates. The present note complements their work by obtaining theLp-rates of convergence, 1≦p<∞ forT(Fn)-T(F) and its application toL-estimates.

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References

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Authors and Affiliations

  1. University of Maryland Baltimore County, USA

    Ibrahim A. Ahmad

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  1. Ibrahim A. Ahmad
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Ahmad, I.A. OnLp-convergence rates for statistical functions with application toL-estimates. Ann Inst Stat Math 35, 401–406 (1983). https://doi.org/10.1007/BF02480996

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  • DOI: https://doi.org/10.1007/BF02480996

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