Empirical Bayes Estimates of Domain Scores Under Binomial and Hypergeometric Distributions for Test Scores
Authors: Lin Miao-Hsiang , Hsiung Chao A. 
Published: February 2006

We introduce two simple empirical approximate Bayes estimators (EABEs)— \documentclass[12pt]{minimal}
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$$\widetilde{d}_N (x)$$
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$$\widetilde\delta _N (x)$$
\end{document}—for estimating domain scores under binomial and hypergeometric distributions, respectively. Both EABEs (derived from corresponding marginal distributions of observed test score x without relying on knowledge of prior domain score distributions) have been proven to hold Δ-asymptotic optimality in Robbins' sense of convergence in mean. We found that, where \documentclass[12pt]{minimal}
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$$\widetilde{d}^* _N$$
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$$\widetilde\delta ^* _N$$
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$$\widetilde{d}_N$$
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$$\widetilde\delta _N$$
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$$\widetilde{d}^* _N$$
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$$\widetilde\delta ^* _N$$
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$$\widetilde{d}^* _N$$
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$$\widetilde\delta ^* _N$$
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$$\widetilde\delta ^* _N$$
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$$\widetilde{d}^* _N$$
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$$\widetilde{d}^* _N$$
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$$\widetilde\delta ^* _N$$
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