More Higher-Order Efficiency: Concentration Probability
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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Volume (Year): 67 (1998)
Issue (Month): 2 (November)
Pages: 349-366
| Handle: | RePEc:eee:jmvana:v:67:y:1998:i:2:p:349-366 |
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References listed on IDEAS
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- Magnus, J.R. & Neudecker, H., 1985. "Matrix differential calculus with applications to simple, Hadamard, and Kronecker products," Other publications TiSEM 1b2f1740-bfd1-4ea5-986c-9, Tilburg University, School of Economics and Management.
- 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.
- 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.
- Yuzo Hosoya, 1990. "Information amount and higher-order efficiency in estimation," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 42(1), pages 37-49, March.
- 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.
- 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.
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