Adaptive Quantile Computation for Brownian Bridge in Change-Point Analysis

As an example for the fast calculation of distributional parameters of Gaussian processes, we propose a new Monte Carlo algorithm for the computation of quantiles of the supremum norm of weighted Brownian bridges. As it is known, the corresponding distributions arise asymptotically for weighted CUSU...

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Bibliographic Details
Published inarXiv.org
Main Authors Franke, Jürgen, Hefter, Mario, Herzwurm, André, Ritter, Klaus, Schwaar, Stefanie
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 31.12.2020
Subjects
Adaptive algorithms
Algorithms
Brownian motion
Computation
Discretization
Gaussian process
Process parameters
Quantiles
Stochastic processes
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Summary:As an example for the fast calculation of distributional parameters of Gaussian processes, we propose a new Monte Carlo algorithm for the computation of quantiles of the supremum norm of weighted Brownian bridges. 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.
ISSN:2331-8422