Asymptotic properties of the Bayes and pseudo Bayes estimators of ability in item response theory

Authors:
Haruhiko Ogasawara
Affiliations:
-
Venue:
Journal of Multivariate Analysis
Year:
2013

Citing 2
Cited 0

Asymptotic cumulants of the parameter estimators in item response theory

Computational Statistics - Proceedings of DSC 2007
Asymptotic expansions for the pivots using log-likelihood derivatives with an application in item response theory

Journal of Multivariate Analysis

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Abstract

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 with the general weight. The asymptotic cumulants of the estimators after studentization are also derived. From the comparison of the mean square errors, the Bayes modal estimator with the standard normal prior is recommended for point estimation. For interval estimation, however, the maximum likelihood estimator is appropriate considering its small bias after studentization.