IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v56y2012i12p4204-4214.html
   My bibliography  Save this article

Diagnostics for a class of survival regression models with heavy-tailed errors

Author

Listed:
  • Li, Ai-Ping
  • Xie, Feng-Chang

Abstract

The heavy-tailed survival regression models provide a useful extension of the normal regression models for data sets involving errors with longer-than-normal tails. This article develops influence diagnostics under case-deletion model (CDM) in survival regression models for which the errors follow the log-generalized Birnbaum–Saunders distribution based on the t model (LBST). The one-step approximations of the estimates in CDM are given and case-deletion measures are obtained. Meanwhile, we discuss a score test for the homogeneity of shape parameter in LBST regression models. One numerical example is given to illustrate our methodology and the properties of the score test statistic are investigated through Monte Carlo simulations under different censoring percentages.

Suggested Citation

  • Li, Ai-Ping & Xie, Feng-Chang, 2012. "Diagnostics for a class of survival regression models with heavy-tailed errors," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4204-4214.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:12:p:4204-4214
    DOI: 10.1016/j.csda.2012.04.015
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S016794731200179X
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2012.04.015?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. Berkane, Maia & Kano, Yutaka & Bentler, Peter M., 1994. "Pseudo maximum likelihood estimation in elliptical theory: Effects of misspecification," Computational Statistics & Data Analysis, Elsevier, vol. 18(2), pages 255-267, September.
    2. Barros, Michelli & Paula, Gilberto A. & Leiva, Víctor, 2009. "An R implementation for generalized Birnbaum-Saunders distributions," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1511-1528, February.
    3. Gilberto A. Paula & Víctor Leiva & Michelli Barros & Shuangzhe Liu, 2012. "Robust statistical modeling using the Birnbaum‐Saunders‐t distribution applied to insurance," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 28(1), pages 16-34, January.
    4. Lucia Santana & Filidor Vilca & V�ctor Leiva, 2011. "Influence analysis in skew-Birnbaum--Saunders regression models and applications," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(8), pages 1633-1649, July.
    5. Jin-Guan Lin & Li-Xing Zhu & Feng-Chang Xie, 2009. "Heteroscedasticity diagnostics for t linear regression models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 70(1), pages 59-77, June.
    6. Tang, Nian-Sheng & Wei, Bo-Cheng & Wang, Xue-Ren, 2000. "Influence diagnostics in nonlinear reproductive dispersion models," Statistics & Probability Letters, Elsevier, vol. 46(1), pages 59-68, January.
    7. Leiva, Victor & Barros, Michelli & Paula, Gilberto A. & Galea, Manuel, 2007. "Influence diagnostics in log-Birnbaum-Saunders regression models with censored data," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5694-5707, August.
    8. Artur J. Lemonte & Alexandre G. Patriota, 2011. "Influence diagnostics in Birnbaum--Saunders nonlinear regression models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(5), pages 871-884, February.
    9. Vilca, Filidor & Santana, Lucia & Leiva, Víctor & Balakrishnan, N., 2011. "Estimation of extreme percentiles in Birnbaum-Saunders distributions," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1665-1678, April.
    10. Galea, Manuel & Paula, Gilberto A. & Cysneiros, Francisco José A., 2005. "On diagnostics in symmetrical nonlinear models," Statistics & Probability Letters, Elsevier, vol. 73(4), pages 459-467, July.
    11. Leiva, Victor & Riquelme, Marco & Balakrishnan, N. & Sanhueza, Antonio, 2008. "Lifetime analysis based on the generalized Birnbaum-Saunders distribution," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 2079-2097, January.
    12. Lemonte, Artur J. & Cribari-Neto, Francisco & Vasconcellos, Klaus L.P., 2007. "Improved statistical inference for the two-parameter Birnbaum-Saunders distribution," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4656-4681, May.
    13. Wang, Zhihui & Desmond, A.F. & Lu, Xuewen, 2006. "Modified censored moment estimation for the two-parameter Birnbaum-Saunders distribution," Computational Statistics & Data Analysis, Elsevier, vol. 50(4), pages 1033-1051, February.
    14. Xie, Feng-Chang & Wei, Bo-Cheng, 2007. "Diagnostics analysis for log-Birnbaum-Saunders regression models," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4692-4706, May.
    15. Lemonte, Artur J. & Ferrari, Silvia L.P., 2011. "Size and power properties of some tests in the Birnbaum-Saunders regression model," Computational Statistics & Data Analysis, Elsevier, vol. 55(2), pages 1109-1117, February.
    16. Bo-Cheng Wei & Jian-Qing Shih, 1994. "On statistical models for regression diagnostics," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(2), pages 267-278, June.
    17. Lemonte, Artur J. & Ferrari, Silvia L.P. & Cribari-Neto, Francisco, 2010. "Improved likelihood inference in Birnbaum-Saunders regressions," Computational Statistics & Data Analysis, Elsevier, vol. 54(5), pages 1307-1316, May.
    18. Kundu, Debasis & Kannan, Nandini & Balakrishnan, N., 2008. "On the hazard function of Birnbaum-Saunders distribution and associated inference," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2692-2702, January.
    19. Gómez, Héctor W. & Olivares-Pacheco, Juan F. & Bolfarine, Heleno, 2009. "An extension of the generalized Birnbaum-Saunders distribution," Statistics & Probability Letters, Elsevier, vol. 79(3), pages 331-338, February.
    20. Feng-Chang Xie & Bo-Cheng Wei & Jin-Guan Lin, 2007. "Case-deletion Influence Measures for the Data from Multivariate t Distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 34(8), pages 907-921.
    21. Ng, H. K. T. & Kundu, D. & Balakrishnan, N., 2003. "Modified moment estimation for the two-parameter Birnbaum-Saunders distribution," Computational Statistics & Data Analysis, Elsevier, vol. 43(3), pages 283-298, July.
    22. Hao Qu & Feng‐Chang Xie, 2011. "Diagnostics analysis for log‐Birnbaum–Saunders regression models with censored data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 65(1), pages 1-21, February.
    23. Manuel Galea & Victor Leiva-Sanchez & Gilberto Paula, 2004. "Influence Diagnostics in log-Birnbaum-Saunders Regression Models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(9), pages 1049-1064.
    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. Lemonte, Artur J., 2013. "A new extended Birnbaum–Saunders regression model for lifetime modeling," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 34-50.
    2. Edwin M. M. Ortega & Artur J. Lemonte & Gauss M. Cordeiro & Vicente G. Cancho & Fábio L. Mialhe, 2018. "Heteroscedastic log-exponentiated Weibull regression model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 45(3), pages 384-408, February.

    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. Lemonte, Artur J., 2013. "A new extended Birnbaum–Saunders regression model for lifetime modeling," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 34-50.
    2. Li, Ai-Ping & Chen, Zhao-Xia & Xie, Feng-Chang, 2012. "Diagnostic analysis for heterogeneous log-Birnbaum–Saunders regression models," Statistics & Probability Letters, Elsevier, vol. 82(9), pages 1690-1698.
    3. Ortega, Edwin M.M. & Cordeiro, Gauss M. & Lemonte, Artur J., 2012. "A log-linear regression model for the β-Birnbaum–Saunders distribution with censored data," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 698-718.
    4. Azevedo, Cecilia & Leiva, Víctor & Athayde, Emilia & Balakrishnan, N., 2012. "Shape and change point analyses of the Birnbaum–Saunders-t hazard rate and associated estimation," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 3887-3897.
    5. Barros, Michelli & Paula, Gilberto A. & Leiva, Víctor, 2009. "An R implementation for generalized Birnbaum-Saunders distributions," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1511-1528, February.
    6. Lemonte, Artur J. & Ferrari, Silvia L.P., 2011. "Size and power properties of some tests in the Birnbaum-Saunders regression model," Computational Statistics & Data Analysis, Elsevier, vol. 55(2), pages 1109-1117, February.
    7. Wang, Bing Xing, 2012. "Generalized interval estimation for the Birnbaum–Saunders distribution," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4320-4326.
    8. Artur J. Lemonte & Alexandre G. Patriota, 2011. "Influence diagnostics in Birnbaum--Saunders nonlinear regression models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(5), pages 871-884, February.
    9. Vanegas, Luis Hernando & Rondón, Luz Marina & Cysneiros, Francisco José A., 2012. "Diagnostic procedures in Birnbaum–Saunders nonlinear regression models," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1662-1680.
    10. Xie, Feng-Chang & Wei, Bo-Cheng, 2007. "Diagnostics analysis for log-Birnbaum-Saunders regression models," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4692-4706, May.
    11. N. Balakrishnan & Xiaojun Zhu, 2015. "Inference for the bivariate Birnbaum–Saunders lifetime regression model and associated inference," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(7), pages 853-872, October.
    12. Marchant, Carolina & Bertin, Karine & Leiva, Víctor & Saulo, Helton, 2013. "Generalized Birnbaum–Saunders kernel density estimators and an analysis of financial data," Computational Statistics & Data Analysis, Elsevier, vol. 63(C), pages 1-15.
    13. Bhatti, Chad R., 2010. "The Birnbaum–Saunders autoregressive conditional duration model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(10), pages 2062-2078.
    14. Lucia Santana & Filidor Vilca & V�ctor Leiva, 2011. "Influence analysis in skew-Birnbaum--Saunders regression models and applications," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(8), pages 1633-1649, July.
    15. Lemonte, Artur J. & Cordeiro, Gauss M., 2009. "Birnbaum-Saunders nonlinear regression models," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4441-4452, October.
    16. Fierro, Raúl & Leiva, Víctor & Ruggeri, Fabrizio & Sanhueza, Antonio, 2013. "On a Birnbaum–Saunders distribution arising from a non-homogeneous Poisson process," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1233-1239.
    17. Xiao, Qingchu & Liu, Zaiming & Balakrishnan, N. & Lu, Xuewen, 2010. "Estimation of the Birnbaum-Saunders regression model with current status data," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 326-332, February.
    18. Barreto, Larissa Santana & Cysneiros, Audrey H.M.A. & Cribari-Neto, Francisco, 2013. "Improved Birnbaum–Saunders inference under type II censoring," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 68-81.
    19. Michelli Barros & Manuel Galea & Manuel González & Víctor Leiva, 2010. "Influence diagnostics in the tobit censored response model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 19(3), pages 379-397, August.
    20. Kundu, Debasis & Balakrishnan, N. & Jamalizadeh, Ahad, 2013. "Generalized multivariate Birnbaum–Saunders distributions and related inferential issues," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 230-244.

    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:csdana:v:56:y:2012:i:12:p:4204-4214. 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/locate/csda .

    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.