On the minimizing point of the incorrectly centered empirical process and its limit distribution in nonregular experiments
Research output: Contribution to journal › Research article › Contributed › peer-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 language | English |
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Pages (from-to) | 307-322 |
Number of pages | 16 |
Journal | Probability and statistics = Probabilités et statistique |
Volume | 9 |
Publication status | Published - Oct 2005 |
Peer-reviewed | Yes |
Keywords
ASJC Scopus subject areas
Keywords
- Argmin-CMT, Poisson-process, Rescaled empirical process, Weak convergence in D(R)