Bootstrap Confidence Intervals Using the Likelihood Ratio Test in Changepoint Detection

TL;DR

This paper evaluates bootstrap-based likelihood ratio tests for changepoint detection, proposing a method to estimate null distributions and calculate confidence intervals to improve test power and accuracy.

Contribution

It introduces a bootstrap approach to construct confidence intervals for changepoint detection, including a method to estimate null distributions assuming no changepoint.

Findings

Bootstrap method effectively estimates changepoint sampling distribution.

Proposed approach improves confidence interval accuracy.

Method enables better power analysis for changepoint tests.

Abstract

This study aims to evaluate the performance of power in the likelihood ratio test for changepoint detection by bootstrap sampling, and proposes a hypothesis test based on bootstrapped confidence interval lengths. Assuming i.i.d normally distributed errors, and using the bootstrap method, the changepoint sampling distribution is estimated. Furthermore, this study describes a method to estimate a data set with no changepoint to form the null sampling distribution. With the null sampling distribution, and the distribution of the estimated changepoint, critical values and power calculations can be made, over the lengths of confidence intervals.