The 'three plus one' likelihood-based test statistics: unified geometrical and graphical interpretations

Gianfranco Lovison, Vito Michele Rosario Muggeo, Vito M. R. Muggeo, Gianfranco Lovison

Risultato della ricerca: Article

5 Citazioni (Scopus)

Abstract

The presentation of the well known Likelihood Ratio, Wald and Score test statistics in textbooks appears to lack a unified graphical and geometrical interpretation. We present two simple graphical representations on a common scale for these three test statistics, and also the recently proposed Gradient test statistic. These unified graphical displays may favour better understanding of the geometrical meaning of the likelihood based statistics and provide useful insights into their connections.
Lingua originaleEnglish
pagine (da-a)302-306
Numero di pagine5
RivistaTHE AMERICAN STATISTICIAN
Volume68
Stato di pubblicazionePublished - 2014

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Test Statistic
Likelihood
Graphical Display
Wald Test
Score Test
Graphical Representation
Likelihood Ratio Test
Gradient
Statistics
Interpretation
Graphics
Test statistic
Presentation
Meaning
Likelihood ratio test
Textbooks
Wald test
Score test

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Mathematics(all)

Cita questo

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abstract = "The presentation of the well known Likelihood Ratio, Wald and Score test statistics in textbooks appears to lack a unified graphical and geometrical interpretation. We present two simple graphical representations on a common scale for these three test statistics, and also the recently proposed Gradient test statistic. These unified graphical displays may favour better understanding of the geometrical meaning of the likelihood based statistics and provide useful insights into their connections.",
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AU - Muggeo, Vito M. R.

AU - Lovison, Gianfranco

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AB - The presentation of the well known Likelihood Ratio, Wald and Score test statistics in textbooks appears to lack a unified graphical and geometrical interpretation. We present two simple graphical representations on a common scale for these three test statistics, and also the recently proposed Gradient test statistic. These unified graphical displays may favour better understanding of the geometrical meaning of the likelihood based statistics and provide useful insights into their connections.

KW - Likelihood ratio, Wald, Score, Gradient statistic, geometrical interpretation, graphical display

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JF - American Statistician

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