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The Geometry of Generalized Likelihood Ratio Test.

Yongqiang Cheng1, Hongqiang Wang1, Xiang Li1

  • 1College of Electronic Science and Engineering, National University of Defense Technology, Changsha 410073, China.

Entropy (Basel, Switzerland)
|December 23, 2022
PubMed
Summary
This summary is machine-generated.

This study explores the generalized likelihood ratio test (GLRT) using information geometry. It offers a new geometric interpretation for composite hypothesis testing and analyzes asymptotic performance.

Keywords:
composite hypothesis testinggeneralized likelihood ratio testinformation geometryinformation lossmaximum likelihood estimationstatistical inference

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Area of Science:

  • Statistics
  • Information Geometry
  • Theoretical Statistics

Background:

  • Composite hypothesis testing is a fundamental problem in statistical inference.
  • The generalized likelihood ratio test (GLRT) is a widely used method for such problems.
  • Existing interpretations of GLRT lack a unified geometric framework.

Purpose of the Study:

  • To provide an information-geometrical interpretation of the GLRT.
  • To develop a geometric understanding of GLRT for composite hypotheses.
  • To analyze the asymptotic performance of GLRT through its geometric representation.

Main Methods:

  • Studying GLRT from a geometric perspective.
  • Utilizing the geometry of curved exponential families.
  • Developing two geometric pictures for different parameter scenarios.
  • Demonstrating with a one-dimensional curved Gaussian distribution.

Main Results:

  • An information-geometrical interpretation of GLRT is proposed.
  • Two distinct geometric visualizations of GLRT are presented.
  • The geometric realization of GLRT is elucidated through a Gaussian distribution example.
  • Asymptotic performance analysis is linked to the geometric representation.

Conclusions:

  • The study offers a novel geometric perspective on GLRT.
  • This geometric approach enhances the theoretical understanding of statistical inference.
  • The findings provide a new framework for analyzing GLRT in composite hypothesis testing.