Adaptive Quantile Computation for Brownian Bridge in Change-Point Analysis

TL;DR

This paper introduces an adaptive Monte Carlo algorithm for efficiently computing quantiles of the supremum norm of weighted Brownian bridges, which are crucial in change-point detection, outperforming traditional methods.

Contribution

The paper presents a novel adaptive discretization method for Brownian bridge quantile computation, improving efficiency over standard uniform discretization approaches.

Findings

The adaptive algorithm significantly outperforms the standard uniform discretization method.

Simulation results demonstrate faster and more accurate quantile estimation.

The method enhances computational efficiency in change-point analysis applications.

Abstract

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.