On the boundedness and nonmonotonicity of generalized score statistics

C. A. Field, Zhen Pang, A. H. Welsh

Research output: Journal article publicationJournal articleAcademic researchpeer-review


We show in the context of the linear regression model fitted by Gaussian quasi-likelihood estimation that the generalized score statistics of Boos and Hu and Kalbfleisch for individual parameters can be bounded and nonmonotone in the parameter, making it difficult tomake inferences from the generalized score statistic. The phenomenon is due to the form of the functional dependence of the estimators on the parameter being held fixed and the way this affects the score function and/or the estimator of the asymptotic variance. We note that in some settings, the score statistic can be bounded and nonmonotone.
Original languageEnglish
Pages (from-to)92-98
Number of pages7
JournalAmerican Statistician
Issue number2
Publication statusPublished - 23 Aug 2012
Externally publishedYes


  • Confidence intervals
  • Estimating equations
  • Quasi-likelihood estimation
  • Score test

ASJC Scopus subject areas

  • General Mathematics
  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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