Inference Functions and Quadratic Score Tests

Bruce G. Lindsay, Annie Qu

Research output: Contribution to journalArticlepeer-review


A general expository description is given of the use of quadratic score test statistics as inference functions. This methodology allows one to do efficient estimation and testing in a semiparametric model defined by a set of mean-zero estimating functions. The inference function is related to a quadratic minimum distance problem. The asymptotic chi-squared properties are shown to be the consequences of asymptotic projection properties. Shortcomings of the asymptotic theory are discussed and a bootstrap method is shown to correct for anticonservative testing behavior.

Original languageEnglish (US)
Pages (from-to)394-410
Number of pages17
JournalStatistical Science
Issue number3
StatePublished - Aug 2003
Externally publishedYes


  • Bootstrapping
  • Chi-squared test
  • Edgeworth expansion
  • Generalized estimating equation
  • Generalized method of moments
  • Likelihood
  • Quadratic inference function
  • Quasi-likelihood
  • Semiparametric model

ASJC Scopus subject areas

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


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