IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v63y2003i4p375-385.html
   My bibliography  Save this article

PMSE dominance of the positive-part shrinkage estimator in a regression model when relevant regressors are omitted

Author

Listed:
  • Namba, Akio

Abstract

In this paper, we consider a regression model with omitted relevant regressors and a general family of shrinkage estimators of regression coefficients. We derive the formula for the predictive mean squared error (PMSE) of the estimators. It is shown analytically that the positive-part shrinkage estimator dominates the ordinary shrinkage estimator even when there are omitted relevant regressors. Also, as an example, our result is applied to the double k-class estimator.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:63:y:2003:i:4:p:375-385
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(03)00103-2
    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. Nickerson, David M., 1988. "Dominance of the positive-part version of the James-Stein estimator," Statistics & Probability Letters, Elsevier, vol. 7(2), pages 97-103, September.
    2. Namba, Akio, 2002. "Pmse Performance Of The Biased Estimators In A Linear Regression Model When Relevant Regressors Are Omitted," Econometric Theory, Cambridge University Press, vol. 18(5), pages 1086-1098, October.
    3. Ohtani, Kazuhiro, 1993. "A Comparison of the Stein-Rule and Positive-Part Stein-Rule Estimators in a Misspecified Linear Regression Model," Econometric Theory, Cambridge University Press, vol. 9(4), pages 668-679, August.
    4. Ullah, Aman & Ullah, Shobha, 1978. "Double k-Class Estimators of Coefficients in Linear Regression," Econometrica, Econometric Society, vol. 46(3), pages 705-722, May.
    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. Namba, Akio & Ohtani, Kazuhiro, 2006. "PMSE performance of the Stein-rule and positive-part Stein-rule estimators in a regression model with or without proxy variables," Statistics & Probability Letters, Elsevier, vol. 76(9), pages 898-906, May.

    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. Namba, Akio & Ohtani, Kazuhiro, 2006. "PMSE performance of the Stein-rule and positive-part Stein-rule estimators in a regression model with or without proxy variables," Statistics & Probability Letters, Elsevier, vol. 76(9), pages 898-906, May.
    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. Akio Namba & Kazuhiro Ohtani, 2007. "Risk comparison of the Stein-rule estimator in a linear regression model with omitted relevant regressors and multivariatet errors under the Pitman nearness criterion," Statistical Papers, Springer, vol. 48(1), pages 151-162, January.
    4. 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.
    5. 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.
    6. 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.
    7. A. Saleh & B. Golam Kibria, 2011. "On some ridge regression estimators: a nonparametric approach," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(3), pages 819-851.
    8. 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.
    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. Ullah, A. & Vinod, H. D. & Kadiyala, R. K., 1978. "A Family Of Improved Ordinary Ridge Estimators," Econometric Institute Archives 272169, Erasmus University Rotterdam.
    11. 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.
    12. Shalabh, & Garg, G. & Heumann, C., 2012. "Performance of double k-class estimators for coefficients in linear regression models with non-spherical disturbances under asymmetric losses," Journal of Multivariate Analysis, Elsevier, vol. 112(C), pages 35-47.
    13. Ohtani, Kazuhiro & Kozumi, Hideo, 1996. "The exact general formulae for the moments and the MSE dominance of the Stein-rule and positive-part Stein-rule estimators," Journal of Econometrics, Elsevier, vol. 74(2), pages 273-287, October.
    14. 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.
    15. Ohtani, Kazuhiro, 1996. "Further improving the Stein-rule estimator using the Stein variance estimator in a misspecified linear regression model," Statistics & Probability Letters, Elsevier, vol. 29(3), pages 191-199, September.
    16. Kazuhiro Ohtani, 1998. "An MSE comparison of the restricted Stein-rule and minimum mean squared error estimators in regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 7(2), pages 361-376, December.
    17. 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.
    18. Ohtani, Kazuhiro, 2002. "Exact distribution of a pre-test estimator for regression error variance when there are omitted variables," Statistics & Probability Letters, Elsevier, vol. 60(2), pages 129-140, November.
    19. 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.
    20. 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.

    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:stapro:v:63:y:2003:i:4:p:375-385. 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.