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Dependence and independence: Structure and inference.

Albert Vexler1, Xiwei Chen1, Alan D Hutson1

  • 1Department of Biostatistics, The State University of New York at Buffalo, Buffalo, NY, USA.

Statistical Methods in Medical Research
|August 1, 2015
PubMed
Summary
This summary is machine-generated.

This study reviews classical and novel tests of independence, introducing a new dependence index based on Kendall plots. It also presents graphical methods for comparing test powers and understanding dependence structures.

Keywords:
Data-driven testPearson’s correlation coefficientdependence measureempirical likelihoodrandom effectrank testtest of independence

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Area of Science:

  • Statistics
  • Data Analysis

Background:

  • Testing for independence is crucial for analyzing relationships between variables.
  • Classical tests of independence can fail in complex scenarios, necessitating advanced methods.

Purpose of the Study:

  • To provide a comprehensive review and comparison of existing and novel tests of independence.
  • To investigate dependence structures, including those with random effects.
  • To propose new graphical methods for visualizing and assessing dependence.

Main Methods:

  • Review and comparison of classical and novel statistical tests for independence.
  • Investigation of dependence structures with additive and multiplicative random effects.
  • Development of a novel dependence index using the area under the Kendall plot.
  • Application of graphical methodologies, including scatterplots, Kendall plots, and heat maps.

Main Results:

  • Identified scenarios where classical independence tests may be inadequate.
  • Proposed a new index of dependence offering a comprehensive data visualization tool.
  • Demonstrated the effectiveness of heat maps for comparing test powers.
  • Illustrated practical applications of various independence tests and graphical representations.

Conclusions:

  • The proposed novel dependence index and graphical methods enhance the understanding of dependence structures.
  • The study offers practical insights for applied and theoretical research involving independence testing.
  • Advanced methods are essential for robust analysis of complex dependence structures.