Bootstrap for change point detection

TL;DR

This paper introduces a bootstrap method to empirically estimate the distribution of the Likelihood Ratio Test statistic in change point detection, improving calibration and convergence analysis for sequential data analysis.

Contribution

It proposes a bootstrap procedure that convolves likelihood components with random weights, enabling empirical estimation of the LRT distribution in change point detection.

Findings

Bootstrap method converges to the true LRT distribution

Provides theoretical convergence rates for the bootstrap estimator

Enhances change point detection accuracy with empirical calibration

Abstract

In Change point detection task Likelihood Ratio Test (LRT) is sequentially applied in a sliding window procedure. Its high values indicate changes of parametric distribution in the data sequence. Correspondingly LRT values require predefined bound for their maximum. The maximum value has unknown distribution and may be calibrated with multiplier bootstrap. Bootstrap procedure convolves independent components of the Likelihood function with random weights, that enables to estimate empirically LRT distribution. For this empirical distribution of the LRT we show convergence rates to the real maximum value distribution.