IDEAS home Printed from https://ideas.repec.org/a/spr/metrik/v77y2014i6p733-752.html
   My bibliography  Save this article

Shrinkage estimation for the mean of the inverse Gaussian population

Author

Listed:
  • Tiefeng Ma
  • Shuangzhe Liu
  • S. Ahmed

Abstract

We consider improved estimation strategies for a two-parameter inverse Gaussian distribution and use a shrinkage technique for the estimation of the mean parameter. In this context, two new shrinkage estimators are suggested and demonstrated to dominate the classical estimator under the quadratic risk with realistic conditions. Furthermore, based on our shrinkage strategy, a new estimator is proposed for the common mean of several inverse Gaussian distributions, which uniformly dominates the Graybill–Deal type unbiased estimator. The performance of the suggested estimators is examined by using simulated data and our shrinkage strategies are shown to work well. The estimation methods and results are illustrated by two empirical examples. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Tiefeng Ma & Shuangzhe Liu & S. Ahmed, 2014. "Shrinkage estimation for the mean of the inverse Gaussian population," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(6), pages 733-752, August.
    • Handle: RePEc:spr:metrik:v:77:y:2014:i:6:p:733-752
    DOI: 10.1007/s00184-013-0462-8
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00184-013-0462-8
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00184-013-0462-8?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. MacGibbon, Brenda & Shorrock, Glenn, 1997. "Shrinkage estimators for the dispersion parameter of the inverse Gaussian distribution," Statistics & Probability Letters, Elsevier, vol. 32(2), pages 207-214, March.
    2. Yuzo Maruyama & William Strawderman, 2005. "Necessary conditions for dominating the James-Stein estimator," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 57(1), pages 157-165, March.
    3. Ye, Ren-Dao & Ma, Tie-Feng & Wang, Song-Gui, 2010. "Inferences on the common mean of several inverse Gaussian populations," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 906-915, April.
    4. Antonio Sanhueza & Víctor Leiva & N. Balakrishnan, 2008. "A new class of inverse Gaussian type distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 68(1), pages 31-49, June.
    5. Hiroki Masuda, 2009. "Notes on estimating inverse-Gaussian and gamma subordinators under high-frequency sampling," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(1), pages 181-195, March.
    6. Raheem, S.M. Enayetur & Ahmed, S. Ejaz & Doksum, Kjell A., 2012. "Absolute penalty and shrinkage estimation in partially linear models," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 874-891.
    7. Ramesh Gupta & H. Akman, 1995. "Bayes estimation in a mixture inverse Gaussian model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(3), pages 493-503, September.
    8. Chiou, Paul & Miao, Weiwen, 2005. "Shrinkage estimation for the difference between exponential guarantee time parameters," Computational Statistics & Data Analysis, Elsevier, vol. 48(3), pages 489-507, March.
    9. Manzoor Ahmad & Y. Chaubey & B. Sinha, 1991. "Estimation of a common mean of several univariate inverse Gaussian populations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 43(2), pages 357-367, June.
    10. Hsieh, H. K. & Korwar, R. M. & Rukhin, A. L., 1990. "inadmissibility of the maximum likelihood estimator of the inverse gaussian mean," Statistics & Probability Letters, Elsevier, vol. 9(1), pages 83-90, January.
    11. Kuriki, Satoshi & Takemura, Akimichi, 2000. "Shrinkage Estimation towards a Closed Convex Set with a Smooth Boundary," Journal of Multivariate Analysis, Elsevier, vol. 75(1), pages 79-111, October.
    12. Gao, Jinxin & Hitchcock, David B., 2010. "James-Stein shrinkage to improve k-means cluster analysis," Computational Statistics & Data Analysis, Elsevier, vol. 54(9), pages 2113-2127, September.
    13. Fisher, Thomas J. & Sun, Xiaoqian, 2011. "Improved Stein-type shrinkage estimators for the high-dimensional multivariate normal covariance matrix," Computational Statistics & Data Analysis, Elsevier, vol. 55(5), pages 1909-1918, May.
    14. 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.
    15. Tutz, Gerhard & Leitenstorfer, Florian, 2006. "Response shrinkage estimators in binary regression," Computational Statistics & Data Analysis, Elsevier, vol. 50(10), pages 2878-2901, June.
    16. Tiefeng Ma & Shuangzhe Liu, 2013. "Estimation of order-restricted means of two normal populations under the LINEX loss function," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(3), pages 409-425, April.
    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. Khan, Nida & Aslam, Muhammad, 2019. "Statistical Analysis of Location Parameter of Inverse Gaussian Distribution Under Noninformative Priors," Journal of Quantitative Methods, University of Management and Technology, Lahore, Pakistan, vol. 3(2), pages 62-76.
    2. Samadrita Bera & Nabakumar Jana, 2022. "On estimating common mean of several inverse Gaussian distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(1), pages 115-139, January.

    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. Kourouklis, Stavros, 1997. "A new property of the inverse Gaussian distribution with applications," Statistics & Probability Letters, Elsevier, vol. 32(2), pages 161-166, March.
    2. Grzesiek, Aleksandra & Połoczański, Rafał & Kumar, Arun & Wyłomańska, Agnieszka, 2021. "Moment-based estimation for parameters of general inverse subordinator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 575(C).
    3. Tatsuya Kubokawa & Muni S. Srivastava, 2013. "Optimal Ridge-type Estimators of Covariance Matrix in High Dimension," CIRJE F-Series CIRJE-F-906, CIRJE, Faculty of Economics, University of Tokyo.
    4. Leiva, Víctor & Hernández, Hugo & Sanhueza, Antonio, 2008. "An R Package for a General Class of Inverse Gaussian Distributions," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 26(i04).
    5. S. Hossain & S. Ejaz Ahmed & Grace Y. Yi & B. Chen, 2016. "Shrinkage and pretest estimators for longitudinal data analysis under partially linear models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(3), pages 531-549, September.
    6. Tae-Hwan Kim & Christophe Muller, 2020. "Inconsistency transmission and variance reduction in two-stage quantile regression," Post-Print hal-02084505, HAL.
    7. Yang, Guangren & Liu, Yiming & Pan, Guangming, 2019. "Weighted covariance matrix estimation," Computational Statistics & Data Analysis, Elsevier, vol. 139(C), pages 82-98.
    8. Tsukuma, Hisayuki, 2016. "Estimation of a high-dimensional covariance matrix with the Stein loss," Journal of Multivariate Analysis, Elsevier, vol. 148(C), pages 1-17.
    9. Yuzo Maruyama & William Strawderman, 2005. "Necessary conditions for dominating the James-Stein estimator," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 57(1), pages 157-165, March.
    10. Brett Naul & Bala Rajaratnam & Dario Vincenzi, 2016. "The role of the isotonizing algorithm in Stein’s covariance matrix estimator," Computational Statistics, Springer, vol. 31(4), pages 1453-1476, December.
    11. 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.
    12. Stephen S. M. Lee & Mehdi Soleymani, 2015. "A Simple Formula for Mixing Estimators With Different Convergence Rates," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1463-1478, December.
    13. Dominique Fourdrinier & William Strawderman & Martin Wells, 2006. "Estimation of a Location Parameter with Restrictions or “vague information” for Spherically Symmetric Distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 58(1), pages 73-92, March.
    14. Yuki Ikeda & Tatsuya Kubokawa, 2015. "Linear Shrinkage Estimation of Large Covariance Matrices with Use of Factor Models," CIRJE F-Series CIRJE-F-958, CIRJE, Faculty of Economics, University of Tokyo.
    15. Arnab Chakrabarti & Rituparna Sen, 2018. "Some Statistical Problems with High Dimensional Financial data," Papers 1808.02953, arXiv.org.
    16. Lee, Kyoungjae & Jo, Seongil & Lee, Jaeyong, 2022. "The beta-mixture shrinkage prior for sparse covariances with near-minimax posterior convergence rate," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
    17. T. Thomson & S. Hossain, 2018. "Efficient Shrinkage for Generalized Linear Mixed Models Under Linear Restrictions," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(2), pages 385-410, August.
    18. Shi, Jian-Hong & Lv, Jiang-Long, 2012. "A new generalized p-value for testing equality of inverse Gaussian means under heterogeneity," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 96-102.
    19. Martinez-Sanchis, Elena & Mora, Juan & Kandemir, Ilker, 2012. "Counterfactual distributions of wages via quantile regression with endogeneity," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3212-3229.
    20. Cuizhen Niu & Xu Guo & Wangli Xu & Lixing Zhu, 2014. "Testing equality of shape parameters in several inverse Gaussian populations," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(6), pages 795-809, 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:spr:metrik:v:77:y:2014:i:6:p:733-752. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.