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Unbiased Estimation of the MSE Matrix of Stein-Rule Estimators, Confidence Ellipsoids, and Hypothesis Testing

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  • Carter, R.A.L.
  • Srivastava, M.S.
  • Srivastava, V.K.
  • Ullah, A.

Abstract

We first present an unbiased estimator of the MSE matrix of the Stein-rule estimator of the coefficient vector in a normal linear regression model. The Steinrule estimator can be used with both its estimated MSE matrix and with the least-squares MSE matrix to form confidence ellipsoids. We derive the approximate expected squared volumes and coverage probabilities of these confidence sets and discuss their ranking. These results can be applied to the conditional prediction of the mean of the endogenous variable. We also consider the power of F-tests which employ the Stein-rule estimator in place of the least-squares estimator.

Suggested Citation

  • Carter, R.A.L. & Srivastava, M.S. & Srivastava, V.K. & Ullah, A., 1990. "Unbiased Estimation of the MSE Matrix of Stein-Rule Estimators, Confidence Ellipsoids, and Hypothesis Testing," Econometric Theory, Cambridge University Press, vol. 6(1), pages 63-74, March.
    • Handle: RePEc:cup:etheor:v:6:y:1990:i:01:p:63-74_00
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    Cited by:

    1. Kazimi, Camilla & Brownstone, David, 1999. "Bootstrap confidence bands for shrinkage estimators," Journal of Econometrics, Elsevier, vol. 90(1), pages 99-127, May.
    2. Chaturvedi, Anoop & Gupta, Suchita & Bhatti, M. Ishaq, 2012. "Confidence ellipsoids based on a general family of shrinkage estimators for a linear model with non-spherical disturbances," Journal of Multivariate Analysis, Elsevier, vol. 104(1), pages 140-158, February.
    3. Kubokawa, T. & Srivastava, M. S., 2002. "Estimating Risk and the Mean Squared Error Matrix in Stein Estimation," Journal of Multivariate Analysis, Elsevier, vol. 82(1), pages 39-64, July.
    4. Boot, Tom, 2023. "Joint inference based on Stein-type averaging estimators in the linear regression model," Journal of Econometrics, Elsevier, vol. 235(2), pages 1542-1563.
    5. H. Toutenburg & V. K. Srivastava & C. Heumann, 2006. "Application of Stein-Rule Estimation to Linear Regression Models with Some Missing Observations," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 4(2), pages 14-24, July.

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