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  • Kano, Yutaka
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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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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 67 (1998)
    Issue (Month): 2 (November)
    Pages: 349-366

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    Handle: RePEc:eee:jmvana:v:67:y:1998:i:2:p:349-366

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    Related research

    Keywords: bias-adjustment curved exponential distributions Edgeworth expansion maximum likelihood estimator Fisher-consistency;

    References

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    1. Yuzo Hosoya, 1990. "Information amount and higher-order efficiency in estimation," Annals of the Institute of Statistical Mathematics, Springer, vol. 42(1), pages 37-49, March.
    2. Taniguchi, Masanobu, 1986. "Third order asymptotic properties of maximum likelihood estimators for Gaussian ARMA processes," Journal of Multivariate Analysis, Elsevier, vol. 18(1), pages 1-31, February.
    3. Rao C. R. & Sinha Β. K. & Subramanyam K., 1982. "Third Order Efficiency Of The Maximum Likelihood Estimator In The Multinomial Distribution," Statistics & Risk Modeling, De Gruyter, vol. 1(1), pages 1-16, January.
    4. Takeuchi, Kei & Morimune, Kimio, 1985. "Third-Order Efficiency of the Extended Maximum Likelihood Estimators in a Simultaneous Equation System," Econometrica, Econometric Society, vol. 53(1), pages 177-200, January.
    5. Magnus, J.R. & Neudecker, H., 1985. "Matrix differential calculus with applications to simple, Hadamard, and Kronecker products," Open Access publications from Tilburg University urn:nbn:nl:ui:12-153214, Tilburg University.
    6. Pfanzagl, J. & Wefelmeyer, W., 1978. "A third-order optimum property of the maximum likelihood estimator," Journal of Multivariate Analysis, Elsevier, vol. 8(1), pages 1-29, March.
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