Summary
Third order asymptotic efficiency of the maximum likelihood estimator (MLE) has been discussed by J.Pfanzagl and W.Wefelmeyer [34], (who adopted the terminology) and also by J.K.Ghosh and K.Subramanyam [21], for cases where sufficient statistics exist. In this section we shall establish more general results for the multiparameter exponential family, introducing a differential operator, and show that (modified) MLE is always optimal up to the order n−1 among a similar modified class of estimators.
The method is not resticted to the exponential family and will be applied to more general cases in a subsequent discussion.
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© 1981 Springer-Verlag New York Inc.
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Akahira, M., Takeuchi, K. (1981). Second Order and Third Order Asymptotic Efficiency of the Maximum Likelihood Estimator and other Estimators. In: Asymptotic Efficiency of Statistical Estimators: Concepts and Higher Order Asymptotic Efficiency. Lecture Notes in Statistics, vol 7. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-5927-5_5
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DOI: https://doi.org/10.1007/978-1-4612-5927-5_5
Publisher Name: Springer, New York, NY
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