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On the asymptotic distribution of weighted uniform empirical and quantile processes in the middle and on the tails

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  • Csörgo, Miklós
  • Mason, David M.

Abstract

Let [alpha]n and un be the uniform empirical and quantile processes. We investigate the asymptotic distribution of the suprema of [alpha]n(s)/(s(1 - s))1/2±[nu] and un(s)/(s(1 - s))1/2±[nu] with , when the supremum is taken over ranges, depending on n, in the middle of the interval [0, 1], near 0 and near 1. We show that with suitable norming factors the said asymptotic distributions can be radically different or the same, depending on the sign and value of [nu] in the weight function 1/(s(1 - s))1/2±[nu].

Suggested Citation

  • Csörgo, Miklós & Mason, David M., 1985. "On the asymptotic distribution of weighted uniform empirical and quantile processes in the middle and on the tails," Stochastic Processes and their Applications, Elsevier, vol. 21(1), pages 119-132, December.
    • Handle: RePEc:eee:spapps:v:21:y:1985:i:1:p:119-132
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    Cited by:

    1. Einmahl, John H. J., 1997. "Poisson and Gaussian approximation of weighted local empirical processes," Stochastic Processes and their Applications, Elsevier, vol. 70(1), pages 31-58, October.

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