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Testing for a Change in Mean After Changepoint Detection.

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Summary
This summary is machine-generated.

This study introduces a new framework for quantifying uncertainty in time series changepoint detection. The developed methods provide higher powered statistical tests for detecting structural changes in data.

Keywords:
binary segmentationfused lassoselective inferenceℓ0 optimization

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Area of Science:

  • Statistics
  • Time Series Analysis
  • Data Science

Background:

  • Detecting structural changes in time series is common, but quantifying the uncertainty of these detected changes is challenging.
  • Existing methods for changepoint detection often lack robust procedures for post-detection uncertainty estimation.

Purpose of the Study:

  • To develop a novel framework for testing the null hypothesis of no mean change around an estimated changepoint.
  • To provide statistically powerful methods for uncertainty quantification in time series analysis.

Main Methods:

  • Proposed a new framework for hypothesis testing around estimated changepoints.
  • Demonstrated efficient implementation with binary segmentation, ℓ0 segmentation, and fused lasso methods.
  • Developed a setup that conditions on less information for increased test power.

Main Results:

  • The proposed framework successfully quantifies uncertainty in changepoint estimates.
  • The methods yield higher powered statistical tests compared to existing approaches.
  • The framework is efficiently applicable to various changepoint estimation techniques.

Conclusions:

  • The new framework addresses the gap in uncertainty quantification for time series changepoint detection.
  • The R package ChangepointInference facilitates the application of these advanced statistical methods.
  • This work enhances the reliability and interpretability of structural change analysis in time series data.