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Sequential Estimation of the Mean Vector of a Multivariate Linear Process

โœ Scribed by I. Fakhrezakeri; S.Y. Lee

Publisher
Elsevier Science
Year
1993
Tongue
English
Weight
378 KB
Volume
47
Category
Article
ISSN
0047-259X

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โœฆ Synopsis

Sequential procedures are proposed to estimate the unknown mean vector of a multivariate linear process of the form (\mathbf{X}{t}-\boldsymbol{\mu}=\sum{j=0}^{x} A_{j} \mathbf{Z}{i-j}), where the (\mathbf{Z}{i}) 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 (A_{j}), is also obtained. (1993 Academic Press, Inc

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