Volume 9, June 2005
|Page(s)||307 - 322|
|Published online||15 November 2005|
On the minimizing point of the incorrectly centered empirical process and its limit distribution in nonregular experiments
Department of Mathematics, Dresden University of Technology, Helmholtzstr. 10, 01062 Dresden,
Revised: 24 March 2005
Let Fn be the empirical distribution function (df) pertaining to independent random variables with continuous df F. We investigate the minimizing point 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 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.
Mathematics Subject Classification: 60E15 / 60F05 / 60F17 / 62E20
Key words: Rescaled empirical process / argmin-CMT / Poisson-process / weak convergence in D(ℝ).
© EDP Sciences, SMAI, 2005
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