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

Research output: Contribution to journalResearch articleContributedpeer-review

Contributors

Abstract

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.

Details

Original languageEnglish
Pages (from-to)307-322
Number of pages16
JournalProbability and statistics = Probabilités et statistique
Volume9
Publication statusPublished - Oct 2005
Peer-reviewedYes

Keywords

ASJC Scopus subject areas

Keywords

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

Library keywords