Adaptive quantile computation for Brownian bridge in change-point analysis

Jürgen Franke, Mario Hefter, André Herzwurm, Klaus Ritter and Stefanie Schwaar

Computational Statistics & Data Analysis, 2022, vol. 167, issue C

Abstract: As an example for the fast calculation of distributional parameters of Gaussian processes, a new Monte Carlo algorithm for the computation of quantiles of the supremum norm of weighted Brownian bridges is proposed. As it is known, the corresponding distributions arise asymptotically for weighted CUSUM statistics for change-point detection. The new algorithm employs an adaptive (sequential) time discretization for the trajectories of the Brownian bridge. A simulation study shows that the new algorithm by far outperforms the standard approach, which employs a uniform time discretization.

Keywords: Change-point problem; Weighted CUSUM statistic; Weighted Brownian bridge; Sup-norm quantiles; Monte Carlo algorithm; Adaptive discretization (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:167:y:2022:i:c:s0167947321002097

DOI: 10.1016/j.csda.2021.107375

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