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 τ ^ 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 α at a point τ our main result states that n 1/α (τ ^ n -τ) 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 .

DOI : 10.1051/ps:2005014
Classification : 60E15, 60F05, 60F17, 62E20
Mots clés : rescaled empirical process, argmin-CMT, Poisson-process, weak convergence in $D(\mathbb {R})$
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     title = {On the minimizing point of the incorrectly centered empirical process and its limit distribution in nonregular experiments},
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     url = {http://www.numdam.org/articles/10.1051/ps:2005014/}
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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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