Asymptotic approximations to the distributions of the ability estimator and its transformations in item response theory are derived beyond the usual normal one when associated item parameters are given as in tailored testing. For the approximations, the asymptotic cumulants of the estimators up...

The asymptotic cumulants of ability estimators using fallible or estimated item parameters in an ability test based on item response theory are given up to the fourth order with higher-order asymptotic variance. The ability estimators cover those obtained by maximum likelihood, Bayes, and pseudo...

Asymptotic cumulants of the Bayes and pseudo Bayes estimators of ability in item response theory are obtained up to the fourth order with the higher-order asymptotic variance under possible model misspecification. Typical estimators are treated as special cases of the (pseudo) Bayes estimator...