Sequential Estimation of the Mean Vector of a Multivariate Linear Process

I. Fakhrezakeri and S. Y. Lee

Journal of Multivariate Analysis, 1993, vol. 47, issue 2, 196-209

Abstract: Sequential procedures are proposed to estimate the unknown mean vector of a multivariate linear process of the form Xt - [mu] = [summation operator][infinity]j = 0AjZt - j, where the Zt are i.i.d. (0, [Sigma]) with unknown covariance matrix [Sigma]. The proposed point estimation is asymptotically risk efficient in the sense of Starr (1966, Ann. Math. Statist.37 1173-1185). The fixed accuracy confidence set procedure is asymptotically efficient with prescribed coverage probability in the sense of Chow and Robbins (1965, Ann. Math. Statist.36 457-462). A random central limit theorem for this process, under a mild summability condition on the coefficient matrices Aj, is also obtained.

Date: 1993
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