The empirical Bayes approach has become a common method in statistical situations. It is a statistical method for successive Bayes decisions when prior distribution is unknown but many past data are given. The inference for truncation parameters is important for evaluation of upper or lower bounds of population, so it has been studied extensively. Many authors have considered the case of one-sided truncated distribution but in practice, we face the case of two-sided one, too.
Ri Sung Hyon, a section head at the Faculty of Applied Mathematics, has investigated empirical Bayes estimation for truncation parameters of two-sided truncated distribution under squared error loss.
First, he constructed the empirical Bayes estimators of truncation parameters using size two samples and proved the asymptotic optimality of the estimators. Then, he proved that the probability of reverse estimation converges to zero as sample size goes to infinity. Finally, he presented an example to show the soundness of his theoretical results and conducted a simulation on the performance of the proposed empirical Bayes estimators.
The new proposal of using size two samples could be extended to the case of multi-dimensional truncated distributions defined on hyper-cubic domain.
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