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On the minimizing point of the incorrectlycentered empirical process and its limit distributionin 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 F n be the empirical distribution function (df) pertainingto independent random variables with continuous df F. Weinvestigate the minimizing point $\hat\tau_n$ of the empiricalprocess Fn - F0 , where F 0 is another df which differs fromF. If F and F 0 are locally Hölder-continuous of orderα at a point τ our main result states that $n^{1/\alpha}(\hat\tau_n - \tau)$ converges in distribution. Thelimit variable is the almost sure unique minimizing point of atwo-sided time-transformed homogeneous Poisson-process with adrift. The time-transformation and the drift-function are of thetype |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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