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Validity of Edgeworth expansions of minimum contrast estimators for Gaussian ARMA processes

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  • Taniguchi, Masanobu
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    Abstract

    Let {Xt} be a Gaussian ARMA process with spectral density f[theta]([lambda]), where [theta] is an unknown parameter. To estimate [theta] we propose a minimum contrast estimation method which includes the maximum likelihood method and the quasi-maximum likelihood method as special cases. Let [theta][tau] be the minimum contrast estimator of [theta]. Then we derive the Edgewroth expansion of the distribution of [theta][tau] up to third order, and prove its valldity. By this Edgeworth expansion we can see that this minimum contrast estimator is always second-order asymptotically efficient in the class of second-order asymptotically median unbiased estimators. Also the third-order asymptotic comparisons among minimum contrast estimators will be discussed.

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    Bibliographic Info

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

    Volume (Year): 21 (1987)
    Issue (Month): 1 (February)
    Pages: 1-28

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    Handle: RePEc:eee:jmvana:v:21:y:1987:i:1:p:1-28

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    Related research

    Keywords: Gaussian ARMA processes maximum likelihood estimator minimum contrast estimator Edgeworth expansion;

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    Cited by:
    1. Velasco, Carlos & Robinson, Peter M., 2001. "Edgeworth Expansions For Spectral Density Estimates And Studentized Sample Mean," Econometric Theory, Cambridge University Press, vol. 17(03), pages 497-539, June.
    2. Peter M Robinson & Carlos Velasco, 2000. "Edgeworth Expansions for Spectral Density Estimates and Studentized Sample Mean - (Now published in Economic Theory, 17 (2001), pp.497-539," STICERD - Econometrics Paper Series /2000/390, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.

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