IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v133y2015icp266-276.html
   My bibliography  Save this article

Comparisons of variance estimators in a misspecified linear model with elliptically contoured errors

Author

Listed:
  • Hu, Guikai
  • Yu, Shenghua
  • Luo, Han

Abstract

In a misspecified linear regression model with elliptically contoured errors, the exact biases and risks of least squares, restricted least squares, preliminary test and Stein-type estimators of the error variance are derived. Also, we compare the risk performances of the underlying estimators and give the dominance pictures for them. It is shown that the risk of preliminary test estimator attains the smallest value if the critical value equals one. Moreover, we give a bootstrap procedure for estimating the risks of proposed estimators in order to overcome the difficulty of computing the exact risks when the sample size becomes larger.

Suggested Citation

  • Hu, Guikai & Yu, Shenghua & Luo, Han, 2015. "Comparisons of variance estimators in a misspecified linear model with elliptically contoured errors," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 266-276.
    • Handle: RePEc:eee:jmvana:v:133:y:2015:i:c:p:266-276
    DOI: 10.1016/j.jmva.2014.09.012
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X1400219X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2014.09.012?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. 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.
    2. Mittelhammer, R.C., 1984. "Restricted least squares, pre-test, ols and stein rule estimators: Risk comparisons under model misspecification," Journal of Econometrics, Elsevier, vol. 25(1-2), pages 151-164.
    3. Kazuhiro Ohtani & Alan Wan, 2009. "Comparison of the Stein and the usual estimators for the regression error variance under the Pitman nearness criterion when variables are omitted," Statistical Papers, Springer, vol. 50(1), pages 151-160, January.
    4. 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.
    5. Clarke, Judith A. & Giles, David E. A. & Wallace, T. Dudley, 1987. "Preliminary-Test Estimation of the Error Variance in Linear Regression," Econometric Theory, Cambridge University Press, vol. 3(02), pages 299-304, April.
    6. Cambanis, Stamatis & Huang, Steel & Simons, Gordon, 1981. "On the theory of elliptically contoured distributions," Journal of Multivariate Analysis, Elsevier, vol. 11(3), pages 368-385, September.
    7. Arashi, M. & Tabatabaey, S.M.M., 2009. "Improved variance estimation under sub-space restriction," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1752-1760, September.
    8. Zhu, Rong & Zhou, Sherry Z.F., 2011. "Estimating the error variance after a pre-test for an interval restriction on the coefficients," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2312-2323, July.
    9. 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.
    10. M. Arashi & A. Saleh & S. Tabatabaey, 2010. "Estimation of parameters of parallelism model with elliptically distributed errors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 71(1), pages 79-100, January.
    Full references (including those not matched with items on IDEAS)

    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. 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.
    2. M. Arashi & Mahdi Roozbeh, 2019. "Some improved estimation strategies in high-dimensional semiparametric regression models with application to riboflavin production data," Statistical Papers, Springer, vol. 60(3), pages 667-686, June.
    3. Qin, Huaizhen & Ouyang, Weiwei, 2016. "Asymmetric risk of the Stein variance estimator under a misspecified linear regression model," Statistics & Probability Letters, Elsevier, vol. 116(C), pages 94-100.
    4. 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.
    5. 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.
    6. Roozbeh, Mahdi, 2015. "Shrinkage ridge estimators in semiparametric regression models," Journal of Multivariate Analysis, Elsevier, vol. 136(C), pages 56-74.
    7. Falk, Michael, 1998. "A Note on the Comedian for Elliptical Distributions," Journal of Multivariate Analysis, Elsevier, vol. 67(2), pages 306-317, November.
    8. Kume, Alfred & Hashorva, Enkelejd, 2012. "Calculation of Bayes premium for conditional elliptical risks," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 632-635.
    9. Jacob, P. & Suquet, Ch., 1997. "Regression and asymptotical location of a multivariate sample," Statistics & Probability Letters, Elsevier, vol. 35(2), pages 173-179, September.
    10. Tarpey, Thaddeus, 2000. "Parallel Principal Axes," Journal of Multivariate Analysis, Elsevier, vol. 75(2), pages 295-313, November.
    11. Isaac E. Cortés & Osvaldo Venegas & Héctor W. Gómez, 2022. "A Symmetric/Asymmetric Bimodal Extension Based on the Logistic Distribution: Properties, Simulation and Applications," Mathematics, MDPI, vol. 10(12), pages 1-17, June.
    12. Valdez, Emiliano A. & Chernih, Andrew, 2003. "Wang's capital allocation formula for elliptically contoured distributions," Insurance: Mathematics and Economics, Elsevier, vol. 33(3), pages 517-532, December.
    13. Preinerstorfer, David & Pötscher, Benedikt M., 2017. "On The Power Of Invariant Tests For Hypotheses On A Covariance Matrix," Econometric Theory, Cambridge University Press, vol. 33(1), pages 1-68, February.
    14. Peng Ding, 2016. "On the Conditional Distribution of the Multivariate Distribution," The American Statistician, Taylor & Francis Journals, vol. 70(3), pages 293-295, July.
    15. Mittnik, Stefan, 2014. "VaR-implied tail-correlation matrices," Economics Letters, Elsevier, vol. 122(1), pages 69-73.
    16. Jonathan Raimana Chan & Thomas Huckle & Antoine Jacquier & Aitor Muguruza, 2021. "Portfolio optimisation with options," Papers 2111.12658, arXiv.org.
    17. Lombardi, Marco J. & Veredas, David, 2009. "Indirect estimation of elliptical stable distributions," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2309-2324, April.
    18. Fraiman, Ricardo & Moreno, Leonardo & Ransford, Thomas, 2023. "A Cramér–Wold theorem for elliptical distributions," Journal of Multivariate Analysis, Elsevier, vol. 196(C).
    19. Arellano-Valle, Reinaldo B., 2001. "On some characterizations of spherical distributions," Statistics & Probability Letters, Elsevier, vol. 54(3), pages 227-232, October.
    20. Villegas, Cristian & Paula, Gilberto A. & Cysneiros, Francisco José A. & Galea, Manuel, 2013. "Influence diagnostics in generalized symmetric linear models," Computational Statistics & Data Analysis, Elsevier, vol. 59(C), pages 161-170.

    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:133:y:2015:i:c:p:266-276. 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.