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High Dimensional Change Point Inference: Recent Developments and Extensions.

Bin Liu1, Xinsheng Zhang1, Yufeng Liu2

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Summary
This summary is machine-generated.

This study reviews advanced change point analysis for high-dimensional data, crucial for modern fields like genetics and finance. It compares techniques for detecting single or multiple structural breaks in complex datasets.

Keywords:
Alternative patternsChange point detectionHigh dimensionsHypothesis testingMinimax optimalityPrimary 62H15Secondary 62E20

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Area of Science:

  • Statistics
  • Data Science
  • Time Series Analysis

Background:

  • Change point analysis detects structural shifts in data sequences, an active research area since the 1950s.
  • High-dimensional data is now common in economics, finance, genetics, and engineering, rendering older methods insufficient.
  • Detecting change points in high-dimensional data sequences is a significant and challenging task.

Purpose of the Study:

  • To review and compare state-of-the-art techniques for change point testing in high-dimensional mean vectors.
  • To survey extensions for general high-dimensional parameters beyond mean vectors.
  • To explore strategies for testing multiple change points in high dimensions.

Main Methods:

  • Focus on models with at most one change point.
  • Review recent techniques for high-dimensional mean vector change point testing.
  • Compare theoretical properties of existing methods.

Main Results:

  • Identified and compared current leading methods for high-dimensional change point detection.
  • Discussed extensions to parameters beyond mean vectors.
  • Surveyed approaches for multiple change point detection in high dimensions.

Conclusions:

  • The paper provides a comprehensive overview of current methods for high-dimensional change point analysis.
  • It highlights limitations of existing methods and suggests future research directions.
  • Addresses the growing need for robust change point detection in complex, high-dimensional datasets.