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

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  • Ferger, Dietmar

Abstract

Let T be the point, where a reflected Brownian bridge attains its maximal value M. We determine the density and the distribution function of R≔M∕T(1−T). Its counterpart Rn for tied-down sums pertaining to i.i.d. random variables converges in distribution to R. This enables the construction of a change-point test. Our new test performs significantly better than the well-known maximum-type test statistics.

Suggested Citation

  • Ferger, Dietmar, 2018. "On the supremum of a Brownian bridge standardized by its maximizing point with applications to statistics," Statistics & Probability Letters, Elsevier, vol. 134(C), pages 63-69.
    • Handle: RePEc:eee:stapro:v:134:y:2018:i:c:p:63-69
    DOI: 10.1016/j.spl.2017.10.008
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    Cited by:

    1. Steland, Ansgar, 2020. "Testing and estimating change-points in the covariance matrix of a high-dimensional time series," Journal of Multivariate Analysis, Elsevier, vol. 177(C).

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