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Confidence ellipsoids based on a general family of shrinkage estimators for a linear model with non-spherical disturbances

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  • Chaturvedi, Anoop
  • Gupta, Suchita
  • Bhatti, M. Ishaq

Abstract

This paper considers a general family of Stein rule estimators for the coefficient vector of a linear regression model with nonspherical disturbances, and derives estimators for the Mean Squared Error (MSE) matrix, and risk under quadratic loss for this family of estimators. The confidence ellipsoids for the coefficient vector based on this family of estimators are proposed, and the performance of the confidence ellipsoids under the criterion of coverage probability and expected volumes is investigated. The results of a numerical simulation are presented to illustrate the theoretical findings, which could be applicable in the area of economic growth modeling.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:104:y:2012:i:1:p:140-158
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    References listed on IDEAS

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    1. 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.
    2. Chaturvedi, Anoop & Hasegawa, Hikaru & Chaturvedi, Ajit & Shukla, Govind, 1997. "Confidence Sets for the Coefficients Vector of a Linear Regression Model with Nonspherical Disturbances," Econometric Theory, Cambridge University Press, vol. 13(3), pages 406-429, June.
    3. Ullah, Aman & Ullah, Shobha, 1978. "Double k-Class Estimators of Coefficients in Linear Regression," Econometrica, Econometric Society, vol. 46(3), pages 705-722, May.
    4. Tran Hoa, 2005. "Modelling the Impact of China's WTO Membership on Its Investment and Growth: A New Flexible Keynesian Approach," Contributions to Economics, in: Günter S. Heiduk & Kar-yiu Wong (ed.), WTO and World Trade, pages 251-265, Springer.
    5. Van Hoa, Tran, 1985. "The inadmissibility of the Stein estimator in normal multiple regression equations," Economics Letters, Elsevier, vol. 19(1), pages 39-42.
    6. Alan Wan & Anoop Chaturvedi & Guohuazou Zou, 2003. "Unbiased estimation of the MSE matrices of improved estimators in linear regression," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(2), pages 173-189.
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    Cited by:

    1. Yiguo Sun & Ximing Wu, 2018. "Leverage and Volatility Feedback Effects and Conditional Dependence Index: A Nonparametric Study," JRFM, MDPI, vol. 11(2), pages 1-20, June.
    2. Muhammad Aslam & Mehreen Afzaal & M. Ishaq Bhatti, 2021. "A study on exponentiated Gompertz distribution under Bayesian discipline using informative priors," Statistics in Transition New Series, Polish Statistical Association, vol. 22(4), pages 101-119, December.
    3. Aslam Muhammad & Afzaal Mehreen & Ishaq Bhatti M., 2021. "A study on exponentiated Gompertz distribution under Bayesian discipline using informative priors," Statistics in Transition New Series, Statistics Poland, vol. 22(4), pages 101-119, December.

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