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On Bahadur asymptotic efficiency of the maximum likelihood and quasi-maximum likelihood estimators in Gaussian stationary processes

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  • Kakizawa, Yoshihide

Abstract

In this paper the maximum likelihood and quasi-maximum likelihood estimators of a spectral parameter of a mean zero Gaussian stationary process are shown to be asymptotically efficient in the sense of Bahadur under appropriate conditions. In order to obtain exponential convergence rates of tail probabilities of these estimators, a basic result on large deviation probability of certain quadratic form is proved by using several asymptotic properties of Toeplitz matrices. It turns out that the exponential convergence rates of the MLE and qMLE are identical, which depend on the statistical curvature of Gaussian stationary process.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:85:y:2000:i:1:p:29-44
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    References listed on IDEAS

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    1. James Fu & Leon Gleser, 1975. "Classical asymptotic properties of a certain estimator related to the maximum likelihood estimator," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 27(1), pages 213-233, December.
    2. Bercu, B. & Gamboa, F. & Rouault, A., 1997. "Large deviations for quadratic forms of stationary Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 71(1), pages 75-90, October.
    3. 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.
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    Cited by:

    1. Bondon, Pascal, 2009. "Estimation of autoregressive models with epsilon-skew-normal innovations," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1761-1776, September.
    2. Sakiyama, Kenji & Taniguchi, Masanobu, 2004. "Discriminant analysis for locally stationary processes," Journal of Multivariate Analysis, Elsevier, vol. 90(2), pages 282-300, August.

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