IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v104y2012i1p140-158.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X11001473
    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.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    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, Polish Statistical Association, vol. 22(4), pages 101-119, December.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Tran Van Hoa, 2002. "WTO Membership for China and Its Impact on Growth, Investment and Consumption: A New Flexible Keynesian Approach," Economics Working Papers wp02-04, School of Economics, University of Wollongong, NSW, Australia.
    3. Tran Van Hoa, 2003. "Growth of Asian Regional Trade and Income Convergence: Evidence from ASEAN+3 Based on Extended Helpman-Krugman Hypothesis and Flexible Modelling Approach," Economics Working Papers wp03-02, School of Economics, University of Wollongong, NSW, Australia.
    4. Tran Van Hoa, 2000. "Recent Significant Advances in Estimating and Forecasting Theories and Economic Modelling: With Applications to Asian Investment Studies," Economics Working Papers wp00-01, School of Economics, University of Wollongong, NSW, Australia.
    5. Tran Van Hoa, 2003. "New Asian Regionalism: Evidence of ASEAN+3 Free Trade Agreement From Extended Gravity Theory and New Modelling Approach," Economics Working Papers wp03-03, School of Economics, University of Wollongong, NSW, Australia.
    6. Tran Van Hoa, 2004. "Australia-Thailand Free Trade Agreement: Challenges and Opportunities for Bilateral Trade Policy and Closer Economic Relations," Economics Working Papers wp04-12, School of Economics, University of Wollongong, NSW, Australia.
    7. Kazimi, Camilla & Brownstone, David, 1999. "Bootstrap confidence bands for shrinkage estimators," Journal of Econometrics, Elsevier, vol. 90(1), pages 99-127, May.
    8. Akio Namba, 2003. "On the use of the Stein variance estimator in the double k-class estimator when each individual regression coefficient is estimated," Statistical Papers, Springer, vol. 44(1), pages 117-124, January.
    9. Judge G.G. & Mittelhammer R.C., 2004. "A Semiparametric Basis for Combining Estimation Problems Under Quadratic Loss," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 479-487, January.
    10. 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.
    11. Kazuhiro Ohtani & Alan Wan, 2002. "ON THE USE OF THE STEIN VARIANCE ESTIMATOR IN THE DOUBLE k-CLASS ESTIMATOR IN REGRESSION," Econometric Reviews, Taylor & Francis Journals, vol. 21(1), pages 121-134.
    12. Namba, Akio, 2003. "PMSE dominance of the positive-part shrinkage estimator in a regression model when relevant regressors are omitted," Statistics & Probability Letters, Elsevier, vol. 63(4), pages 375-385, July.
    13. Tran Van Hoa & Chaturvedi, A., 1999. "Performance of the 2SHI Estimator under the Generalised Pitman Nearness Criterion," Economics Working Papers wp99-4, School of Economics, University of Wollongong, NSW, Australia.
    14. Akio Namba, 2001. "MSE performance of the 2SHI estimator in a regression model with multivariate t error terms," Statistical Papers, Springer, vol. 42(1), pages 81-96, January.
    15. Pal, Amresh Bahadur & Dubey, Ashutosh Kumar & Chaturvedi, Anoop, 2016. "Shrinkage estimation in spatial autoregressive model," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 362-373.
    16. Zou, Guohua & Wan, Alan T.K. & Wu, Xiaoyong & Chen, Ti, 2007. "Estimation of regression coefficients of interest when other regression coefficients are of no interest: The case of non-normal errors," Statistics & Probability Letters, Elsevier, vol. 77(8), pages 803-810, April.
    17. Chaturvedi, Anoop & Shalabh, 2004. "Risk and Pitman closeness properties of feasible generalized double k-class estimators in linear regression models with non-spherical disturbances under balanced loss function," Journal of Multivariate Analysis, Elsevier, vol. 90(2), pages 229-256, August.
    18. Ohtani, Kazuhiro, 2001. "MSE dominance of the pre-test iterative variance estimator over the iterative variance estimator in regression," Statistics & Probability Letters, Elsevier, vol. 54(3), pages 331-340, October.
    19. Ahmed, S. Ejaz & Nicol, Christopher J., 2012. "An application of shrinkage estimation to the nonlinear regression model," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3309-3321.
    20. Ullah, A. & Vinod, H. D. & Kadiyala, R. K., 1978. "A Family Of Improved Ordinary Ridge Estimators," Econometric Institute Archives 272169, Erasmus University Rotterdam.

    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:104:y:2012:i:1:p:140-158. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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.