IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v47y1993i2p196-209.html
   My bibliography  Save this article

Sequential Estimation of the Mean Vector of a Multivariate Linear Process

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(83)71079-1
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. Lee, Sangyeol, 2003. "The sequential estimation in stochastic regression model with random coefficients," Statistics & Probability Letters, Elsevier, vol. 61(1), pages 71-81, January.
    4. 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.
    5. 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.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:47:y:1993:i:2:p:196-209. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.