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Sequential Estimation of the Mean Vector of a Multivariate Linear Process

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  • Fakhrezakeri, I.
  • Lee, S. Y.

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.

Suggested Citation

  • Fakhrezakeri, I. & Lee, S. Y., 1993. "Sequential Estimation of the Mean Vector of a Multivariate Linear Process," Journal of Multivariate Analysis, Elsevier, vol. 47(2), pages 196-209, November.
    • Handle: RePEc:eee:jmvana:v:47:y:1993:i:2:p:196-209
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    Cited by:

    1. Lee, Sangyeol, 2003. "The sequential estimation in stochastic regression model with random coefficients," Statistics & Probability Letters, Elsevier, vol. 61(1), pages 71-81, January.
    2. Martinsek, Adam T., 2001. "Sequential estimation of the mean in a random coefficient autoregressive model with beta marginals," Statistics & Probability Letters, Elsevier, vol. 51(1), pages 53-61, January.
    3. Lee, Sangyeol & Sriram, T. N., 1999. "Sequential point estimation of parameters in a threshold AR(1) model," Stochastic Processes and their Applications, Elsevier, vol. 84(2), pages 343-355, December.
    4. Shiohama, Takayuki & 塩浜, 敬之 & シオハマ, タカユキ, 2005. "Fixed Size Confidence Regions for Parameters of Stationary Processes Based on a Minimum Contrast Estimator," Discussion Paper 243, Center for Intergenerational Studies, Institute of Economic Research, Hitotsubashi University.
    5. Takayuki Shiohama & Masanobu Taniguchi, 2001. "Sequential Estimation for a Functional of the Spectral Density of a Gaussian Stationary Process," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(1), pages 142-158, March.

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