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Let F n be the empirical distribution function (df) pertaining to independent random variables with continuous df F . We investigate the minimizing point of the empirical process Fn - F0 , where F 0 is another df which differs from F . If F and F 0 are locally Holder-continuous of order α at a point τ our main result states that 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 .

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