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

ESAIM: Probability and Statistics (2005)

- Volume: 9, page 307-322
- ISSN: 1292-8100

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topFerger, Dietmar. "On the minimizing point of the incorrectly centered empirical process and its limit distribution in nonregular experiments." ESAIM: Probability and Statistics 9 (2005): 307-322. <http://eudml.org/doc/245175>.

@article{Ferger2005,

abstract = {Let $F_n$ 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 $F_n - F_0$, 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 $n^\{1/\alpha \}(\hat\{\tau \}_n - \tau )$ 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 $|t|^\{\alpha \}$.},

author = {Ferger, Dietmar},

journal = {ESAIM: Probability and Statistics},

keywords = {rescaled empirical process; argmin-CMT; Poisson-process; weak convergence in $D(\mathbb \{R\})$; Rescaled empirical process; weak convergence in },

language = {eng},

pages = {307-322},

publisher = {EDP-Sciences},

title = {On the minimizing point of the incorrectly centered empirical process and its limit distribution in nonregular experiments},

url = {http://eudml.org/doc/245175},

volume = {9},

year = {2005},

}

TY - JOUR

AU - Ferger, Dietmar

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

JO - ESAIM: Probability and Statistics

PY - 2005

PB - EDP-Sciences

VL - 9

SP - 307

EP - 322

AB - Let $F_n$ 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 $F_n - F_0$, 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 $n^{1/\alpha }(\hat{\tau }_n - \tau )$ 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 $|t|^{\alpha }$.

LA - eng

KW - rescaled empirical process; argmin-CMT; Poisson-process; weak convergence in $D(\mathbb {R})$; Rescaled empirical process; weak convergence in

UR - http://eudml.org/doc/245175

ER -

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