Third order asymptotic properties of maximum likelihood estimators for Gaussian ARMA processes
AbstractIn this paper we investigate various third-order asymptotic properties of maximum likelihood estimators for Gaussian ARMA processes by the third-order Edgeworth expansions of the sampling distributions. We define a third-order asymptotic efficiency by the highest probability concentration around the true value with respect to the third-order Edgeworth expansion. Then we show that the maximum likelihood estimator is not always third-order asymptotically efficient in the class A3 of third-order asymptotically median unbiased estimators. But, if we confine our discussions to an appropriate class D ([subset of] A3) of estimators, we can show that appropriately modified maximum likelihood estimator is always third-order asymptotically efficient in D.
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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Multivariate Analysis.
Volume (Year): 18 (1986)
Issue (Month): 1 (February)
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Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description
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