More Higher-Order Efficiency: Concentration Probability

Yutaka Kano

Journal of Multivariate Analysis, 1998, vol. 67, issue 2, 349-366

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.

Keywords: bias-adjustment; curved; exponential; distributions; Edgeworth; expansion; maximum; likelihood; estimator; Fisher-consistency (search for similar items in EconPapers)
Date: 1998
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