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On exponential rates of estimators of the parameter in the first-order autoregressive process

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  • Kakizawa, Yoshihide

Abstract

A closed-form expression for the exponential rate of an estimator in the Gaussian AR(1) process is obtained. This shows that the exponential rates of several famous estimators are all identical. Further it is shown that mean-correction does not affect the large deviation asymptotics.

Suggested Citation

  • Kakizawa, Yoshihide, 1998. "On exponential rates of estimators of the parameter in the first-order autoregressive process," Statistics & Probability Letters, Elsevier, vol. 38(4), pages 355-362, July.
    • Handle: RePEc:eee:stapro:v:38:y:1998:i:4:p:355-362
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    References listed on IDEAS

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    1. Fu, James C., 1985. "On exponential rates of likelihood ratio estimators for location parameters," Statistics & Probability Letters, Elsevier, vol. 3(2), pages 101-105, April.
    2. Yoshihide Kakizawa, 1996. "Third‐Order Asymptotic Properties Of Estimators In Gaussian Arma Processes With Unknown Mean," Journal of Time Series Analysis, Wiley Blackwell, vol. 17(4), pages 367-377, July.
    3. Yoshimichi Ochi, 1983. "Asymptotic Expansions For The Distribution Of An Estimator In The First‐Order Autoregressive Process," Journal of Time Series Analysis, Wiley Blackwell, vol. 4(1), pages 57-67, January.
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    Cited by:

    1. Kakizawa, Yoshihide, 2000. "On Bahadur asymptotic efficiency of the maximum likelihood and quasi-maximum likelihood estimators in Gaussian stationary processes," Stochastic Processes and their Applications, Elsevier, vol. 85(1), pages 29-44, January.

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