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

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

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Abstract

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Let Fn 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 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 ${n}^{1/\alpha }\left({\stackrel{^}{\tau }}_{n}-\tau \right)$ 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|α.

How to cite

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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 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 -

References

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