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Improved Multivariate Prediction in a General Linear Model with an Unknown Error Covariance Matrix

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  • Chaturvedi, Anoop
  • Wan, Alan T. K.
  • Singh, Shri P.

Abstract

This paper deals with the problem of Stein-rule prediction in a general linear model. Our study extends the work of Gotway and Cressie (1993) by assuming that the covariance matrix of the model's disturbances is unknown. Also, predictions are based on a composite target function that incorporates allowance for the simultaneous predictions of the actual and average values of the target variable. We employ large sample asymptotic theory and derive and compare expressions for the bias vectors, mean squared error matrices, and risks based on a quadratic loss structure of the Stein-rule and the feasible best linear unbiased predictors. The results are applied to a model with first order autoregressive disturbances. Moreover, a Monte-Carlo experiment is conducted to explore the performance of the predictors in finite samples.

Suggested Citation

  • Chaturvedi, Anoop & Wan, Alan T. K. & Singh, Shri P., 2002. "Improved Multivariate Prediction in a General Linear Model with an Unknown Error Covariance Matrix," Journal of Multivariate Analysis, Elsevier, vol. 83(1), pages 166-182, October.
    • Handle: RePEc:eee:jmvana:v:83:y:2002:i:1:p:166-182
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    References listed on IDEAS

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    1. Gotway, C. A. & Cressie, N., 1993. "Improved Multivariate Prediction under a General Linear Model," Journal of Multivariate Analysis, Elsevier, vol. 45(1), pages 56-72, April.
    2. Wan, Alan T. K. & Chaturvedi, Anoop, 2001. "Double k-Class Estimators in Regression Models with Non-spherical Disturbances," Journal of Multivariate Analysis, Elsevier, vol. 79(2), pages 226-250, November.
    3. Alan Wan & Anoop Chaturvedi, 2000. "Operational Variants of the Minimum Mean Squared Error Estimator in Linear Regression Models with Non-Spherical Disturbances," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(2), pages 332-342, June.
    4. repec:wop:ubisop:0068 is not listed on IDEAS
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    Citations

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    Cited by:

    1. Liu, Xu-Qing & Wang, Dong-Dong & Rong, Jian-Ying, 2009. "Quadratic prediction problems in multivariate linear models," Journal of Multivariate Analysis, Elsevier, vol. 100(2), pages 291-300, February.
    2. Zhang, Xinyu & Chen, Ti & Wan, Alan T.K. & Zou, Guohua, 2009. "Robustness of Stein-type estimators under a non-scalar error covariance structure," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2376-2388, November.
    3. Gülesen Üstündağ Şiray, 2023. "Simultaneous prediction using target function based on principal components estimator with correlated errors," Statistical Papers, Springer, vol. 64(5), pages 1527-1628, October.
    4. Shalabh,, 2013. "A revisit to efficient forecasting in linear regression models," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 161-170.
    5. Liu, Xu-Qing & Rong, Jian-Ying, 2007. "Quadratic prediction problems in finite populations," Statistics & Probability Letters, Elsevier, vol. 77(5), pages 483-489, March.
    6. Arashi, M. & Kibria, B.M. Golam & Norouzirad, M. & Nadarajah, S., 2014. "Improved preliminary test and Stein-rule Liu estimators for the ill-conditioned elliptical linear regression model," Journal of Multivariate Analysis, Elsevier, vol. 126(C), pages 53-74.

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