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Non-Quadratic Distances in Model Assessment.

Marianthi Markatou1, Yang Chen1

  • 1Department of Biostatistics, University at Buffalo, Buffalo, NY 14214, USA.

Entropy (Basel, Switzerland)
|December 3, 2020
PubMed
Summary

This study explores non-quadratic statistical distances for measuring model adequacy and performing model selection. It details properties of total variation, mixture index of fit, and Kullback-Leibler distances for assessing model misspecification.

Keywords:
Kullback-Leibler distancedivergence measuremixture index of fitmodel assessmentnon-quadratic distancestatistical distancetotal variation

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Area of Science:

  • Statistics
  • Data Science
  • Model Assessment

Background:

  • Model adequacy is crucial for reliable scientific conclusions.
  • Statistical distances offer a natural framework for loss functions in model evaluation.
  • Developing meaningful loss functions is a fundamental challenge.

Purpose of the Study:

  • Investigate non-quadratic statistical distances for model adequacy assessment.
  • Explore their utility in model selection.
  • Understand properties and interpretations of selected distances.

Main Methods:

  • Define statistical distance and its properties.
  • Analyze total variation, mixture index of fit, and Kullback-Leibler distances.
  • Conduct a simulation study to exemplify performance.

Main Results:

  • Non-quadratic distances provide valuable insights into model misspecification.
  • Different distances exhibit unique properties influencing their performance.
  • Simulation results demonstrate practical application potential.

Conclusions:

  • Non-quadratic statistical distances are effective tools for model adequacy and selection.
  • Understanding distance properties aids in choosing appropriate measures for scientific applications.
  • Further exploration can enhance model evaluation methodologies.