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Validity of Edgeworth Expansions of Minimum Constrast Estimators for Gaussian ARMA Processes

机译：高斯aRma过程最小约束估计的Edgeworth展开的有效性

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摘要

Let (X sub t) be a Gaussian Autoregression Multivariant Analysis (ARMA) process with spectral density f sub p (lambda), where p is an unknown parameter. To estimate multivarant analysis we propose a minimum contrast estimation method which includes the maximum likelihood method and the quasi-maximum likelihood ethod as special cases. Let p-bar sub T be the minimum contrast estimator of p. Then we derive the Edgeworth expansion of the distribution of p-bar sub T up to third order, and provide its validity. 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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