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Rényi-type empirical processes

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  • Csörgo, Miklós
  • Horváth, Lajos

Abstract

We develop a theory of asymptotics for Rényi-type weighted empirical and quantile processes and statistics via characterising their possible limiting behaviour in the middle and on the tails. In case of moderate weight functions tail limiting behaviour is found to be Gaussian, while heavily weighted tail empirical and uniform quantile processes are characterised by their respective Poisson process and exponential sums like asymptotic behaviour.

Suggested Citation

  • Csörgo, Miklós & Horváth, Lajos, 1992. "Rényi-type empirical processes," Journal of Multivariate Analysis, Elsevier, vol. 41(2), pages 338-358, May.
    • Handle: RePEc:eee:jmvana:v:41:y:1992:i:2:p:338-358
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