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

Ferger, Dietmar

doi:10.1051/ps:2005014

Ferger, Dietmar

ESAIM: Probability and Statistics, Tome 9 (2005), pp. 307-322

Résumé

Let $F_{n}$ be the empirical distribution function (df) pertaining to independent random variables with continuous df $F$ . We investigate the minimizing point ${\hat{τ}}_{n}$ 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 $n^{1 / α} ({\hat{τ}}_{n} - τ)$ 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 ${| t |}^{α}$ .

MR Zbl

DOI : 10.1051/ps:2005014

Classification : 60E15, 60F05, 60F17, 62E20
Keywords: rescaled empirical process, argmin-CMT, Poisson-process, weak convergence in $D(\mathbb {R})$

@article{PS_2005__9__307_0,
     author = {Ferger, Dietmar},
     title = {On the minimizing point of the incorrectly centered empirical process and its limit distribution in nonregular experiments},
     journal = {ESAIM: Probability and Statistics},
     pages = {307--322},
     year = {2005},
     publisher = {EDP Sciences},
     volume = {9},
     doi = {10.1051/ps:2005014},
     mrnumber = {2174873},
     zbl = {1136.60315},
     language = {en},
     url = {https://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

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