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

ESAIM: Probability and Statistics (2010)

- 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 (2010): 307-322. <http://eudml.org/doc/104339>.

@article{Ferger2010,

abstract = {
Let Fn 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 Fn - F0, where F0 is another df which differs from
F. If F and F0 are locally Hölder-continuous of order
α at a point τ 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|α.
},

author = {Ferger, Dietmar},

journal = {ESAIM: Probability and Statistics},

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

language = {eng},

month = {3},

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/104339},

volume = {9},

year = {2010},

}

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

DA - 2010/3//

PB - EDP Sciences

VL - 9

SP - 307

EP - 322

AB -
Let Fn 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 Fn - F0, where F0 is another df which differs from
F. If F and F0 are locally Hölder-continuous of order
α at a point τ 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|α.

LA - eng

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

UR - http://eudml.org/doc/104339

ER -

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