On the minimizing point of the incorrectly centered empirical process and its limit distribution in nonregular experiments
ESAIM: Probability and Statistics, Tome 9 (2005), pp. 307-322.

Let ${F}_{n}$ be the empirical distribution function (df) pertaining to independent random variables with continuous df $F$. We investigate the minimizing point ${\stackrel{^}{\tau }}_{n}$ of the empirical process ${F}_{n}-{F}_{0}$, where ${F}_{0}$ is another df which differs from $F$. If $F$ and ${F}_{0}$ are locally Hölder-continuous of order $\alpha$ at a point $\tau$ our main result states that ${n}^{1/\alpha }\left({\stackrel{^}{\tau }}_{n}-\tau \right)$ 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 ${|t|}^{\alpha }$.

DOI : https://doi.org/10.1051/ps:2005014
Classification : 60E15,  60F05,  60F17,  62E20
Mots clés : rescaled empirical process, argmin-CMT, Poisson-process, weak convergence in $D\left(ℝ\right)$
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author = {Ferger, Dietmar},
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Ferger, Dietmar. On the minimizing point of the incorrectly centered empirical process and its limit distribution in nonregular experiments. ESAIM: Probability and Statistics, Tome 9 (2005), pp. 307-322. doi : 10.1051/ps:2005014. http://www.numdam.org/articles/10.1051/ps:2005014/

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