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...

Asymptotic cumulants of the Bayes modal estimators of item parameters using marginal likelihood in item response theory are derived up to the fourth order with added higher-order asymptotic variances under possible model misspecification. Among them, only the first asymptotic cumulant and the...