On the supremum of a Brownian bridge standardized by its maximizing point with applications to statistics

摘要

AbstractLetTbe the point, where a reflected Brownian bridge attains its maximal valueM. We determine the density and the distribution function ofR?M∕T(1?T). Its counterpartRnfor tied-down sums pertaining to i.i.d. random variables converges in distribution toR. This enables the construction of a change-point test. Our new test performs significantly better than the well-known maximum-type test statistics.]]>