More Higher-Order Efficiency: Concentration Probability |
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Authors: | Yutaka Kano |
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Institution: | University of Tsukuba, Ibaraki, Japan |
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Abstract: | Based on concentration probability of estimators about a true parameter, third-order asymptotic efficiency of the first-order bias-adjusted MLE within the class of first-order bias-adjusted estimators has been well established in a variety of probability models. In this paper we consider the class of second-order bias-adjusted Fisher consistent estimators of a structural parameter vector on the basis of an i.i.d. sample drawn from a curved exponential-type distribution, and study the asymptotic concentration probability, about a true parameter vector, of these estimators up to the fifth-order. In particular, (i) we show that third-order efficient estimators are always fourth-order efficient; (ii) a necessary and sufficient condition for fifth-order efficiency is provided; and finally (iii) the MLE is shown to be fifth-order efficient. |
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Keywords: | bias-adjustment curved exponential distributions Edgeworth expansion maximum likelihood estimator Fisher-consistency |
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