Validity of Edgeworth Expansions of Minimum Constrast Estimators for Gaussian ARMA Processes.
PITTSBURGH UNIV PA CENTER FOR MULTIVARIATE ANALYSIS
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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.
- Statistics and Probability