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

Published online by Cambridge University Press:  15 November 2005

Dietmar Ferger
Dietmar Ferger*
Affiliation:
Department of Mathematics, Dresden University of Technology, Helmholtzstr. 10, 01062 Dresden, Germany; ferger@math.tu-dresden.de
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Abstract

Let Fn be the empirical distribution function (df) pertaining to independent random variables with continuous df F. We investigate the minimizing point $\hat\tau_n$ 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 $n^{1/\alpha}(\hat\tau_n - \tau)$ 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.

Keywords

Rescaled empirical processargmin-CMTPoisson-processweak convergence in $D(\mathbb{R})$.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 9 , February 2005 , pp. 307 - 322
Copyright
© EDP Sciences, SMAI, 2005

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