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Asymptotic properties of conditional maximum likelihood estimator in a certain exponential model

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  • Fujisawa, Hironori

Abstract

The conditional maximum likelihood estimator is suggested as an alternative to the maximum likelihood estimator and is favorable for an estimator of a dispersion parameter in the normal distribution, the inverse-Gaussian distribution, and so on. However, it is not clear whether the conditional maximum likelihood estimator is asymptotically efficient in general. Consider the case where it is asymptotically efficient and its asymptotic covariance depends only on an objective parameter in an exponential model. This remand implies that the exponential model possesses a certain parallel foliation. In this situation, this paper investigates asymptotic properties of the conditional maximum likelihood estimator and compares the conditional maximum likelihood estimator with the maximum likelihood estimator. We see that the bias of the former is more robust than that of the latter and that two estimators are very close, especially in the sense of bias-corrected version. The mean Pythagorean relation is also discussed.

Suggested Citation

  • Fujisawa, Hironori, 2003. "Asymptotic properties of conditional maximum likelihood estimator in a certain exponential model," Journal of Multivariate Analysis, Elsevier, vol. 86(1), pages 126-142, July.
    • Handle: RePEc:eee:jmvana:v:86:y:2003:i:1:p:126-142
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    References listed on IDEAS

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    1. T. Yanagimoto, 1988. "The conditional maximum likelihood estimator of the shape parameter in the gamma distribution," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 35(1), pages 161-175, December.
    2. Takemi Yanagimoto & Kazuo Anraku, 1989. "Possible superiority of the conditional MLE over the unconditional MLE," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 41(2), pages 269-278, June.
    3. Takemi Yanagimoto, 1991. "Estimating a model through the conditional MLE," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 43(4), pages 735-746, December.
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