Joint consistency of nonparametric item characteristic curve and ability estimation

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The simultaneous and nonparametric estimation of latent abilities and item characteristic curves is considered. The asymptotic properties of ordinal ability estimation and kernel smoothed nonparametric item characteristic curve estimation are investigated under very general assumptions on the underlying item response theory model as both the test length and the sample size increase. A large deviation probability inequality is stated for ordinal ability estimation. The mean squared error of kernel smoothed item characteristic curve estimates is studied and a strong consistency result is obtained showing that the worst case error in the item characteristic curve estimates over all items and ability levels converges to zero with probability equal to one.

Original languageEnglish (US)
Pages (from-to)7-28
Number of pages22
Issue number1
StatePublished - Mar 1997
Externally publishedYes


  • Item characteristic curve
  • Kernel smoothing
  • Large sample theory
  • Nonparametric regression

ASJC Scopus subject areas

  • Mathematics (miscellaneous)
  • Psychology(all)
  • Psychology (miscellaneous)
  • Social Sciences (miscellaneous)

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