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On the minimizing point of the incorrectly centered empirical process and its limit distribution in nonregular experiments
Published online by Cambridge University Press: 15 November 2005
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.
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- Research Article
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- Copyright
- © EDP Sciences, SMAI, 2005
References
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