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The paper makes a critical assessment of Aitchison's criterion of density estimation. It seems not to satisfy certain intuitive requirements. A new criterion based on decisions theoretic considerations is introduced. It is shown through examples that the judgement about the choice of density estimates is seriously dependent on the criterion chosen. Some other density estimates are introduced which look similar to Bayesian predictive density estimates without using a prior distribution.
El-Sayyad et al. (Sun,) studied this question.
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