On the minimizing point of the incorrectly centered empirical process and its limit distribution in nonregular experiments

Research output: Contribution to journalResearch articleContributedpeer-review



Let Fn be the empirical distribution function (df) pertaining to independent random variables with continuous df F. We investigate the minimizing point (formula present) of the empirical process Fn − F0, where F0 is another df which differs from F. If F and F0 are locally Hölder-continuous of order α at a point τ our main result states that (formula present) converges in distribution. The limit variable is the almost sure unique minimizing point of a two-sided time-transformed homogeneous Poisson-process with a drift. The time-transformation and the drift-function are of the type |t|α.


Original languageEnglish
Pages (from-to)307-322
Number of pages16
JournalProbability and statistics = Probabilités et statistique
Publication statusPublished - Oct 2005


ASJC Scopus subject areas


  • Argmin-CMT, Poisson-process, Rescaled empirical process, Weak convergence in D(R)

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