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Weak convergence of empirical and quantile processes in sup-norm metrics via kmt-constructions

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  • Shorack, Galen R.

Abstract

There has been much interest recently in the specially constructed empirical processes of Komlós, Major and Tusnády [2]; as one would guess, much of the application has come from the Hungarian school. In this note we contribute to the unifying effect this profound work has had by showing how the major theorem of O'Reilly [4] follows in rather elementary fashion from this powerful construction. We also take this opportunity to restate O'Reilly's criterion in an elementary form that is far more intelligible.

Suggested Citation

  • Shorack, Galen R., 1979. "Weak convergence of empirical and quantile processes in sup-norm metrics via kmt-constructions," Stochastic Processes and their Applications, Elsevier, vol. 9(1), pages 95-98, August.
    • Handle: RePEc:eee:spapps:v:9:y:1979:i:1:p:95-98
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    Cited by:

    1. Søren Johansen & Bent Nielsen, 2013. "Asymptotic analysis of the Forward Search," Discussion Papers 13-01, University of Copenhagen. Department of Economics.
    2. Ralescu, Stefan S. & Puri, Madan L., 1996. "Weak convergence of sequences of first passage processes and applications," Stochastic Processes and their Applications, Elsevier, vol. 62(2), pages 327-345, July.

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