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Diagnostic analysis for heterogeneous log-Birnbaum–Saunders regression models

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  • Li, Ai-Ping
  • Chen, Zhao-Xia
  • Xie, Feng-Chang
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    Abstract

    In this paper, we introduce a class of heterogeneous log-Birnbaum–Saunders regression models where both the location parameter as well as the shape parameter can be modelled in terms of covariates. The maximum likelihood estimates of parameters are derived. In addition, diagnostic measures are studied based on the case-deletion approach and the local influence approach. Finally, one real example from the medical area is used to illustrate shape parameter modelling and the diagnostic methods.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 82 (2012)
    Issue (Month): 9 ()
    Pages: 1690-1698

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    Handle: RePEc:eee:stapro:v:82:y:2012:i:9:p:1690-1698

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    Related research

    Keywords: Log-Birnbaum–Saunders regression; Heterogeneity; Maximum likelihood estimate; Local influence analysis; Case-deletion;

    References

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    1. 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.
    2. 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, 02.
    3. Hong-Tu Zhu & Sik-Yum Lee, 2001. "Local influence for incomplete data models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(1), pages 111-126.
    4. 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.
    5. 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.
    6. 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.
    7. Cysneiros, Francisco José A. & Paula, Gilberto A. & Galea, Manuel, 2007. "Heteroscedastic symmetrical linear models," Statistics & Probability Letters, Elsevier, vol. 77(11), pages 1084-1090, June.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
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    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. Xu, Dengke & Zhang, Zhongzhan, 2013. "A semiparametric Bayesian approach to joint mean and variance models," Statistics & Probability Letters, Elsevier, vol. 83(7), pages 1624-1631.

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