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Influence diagnostics in nonlinear reproductive dispersion models

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  • Tang, Nian-Sheng
  • Wei, Bo-Cheng
  • Wang, Xue-Ren

Abstract

We extend some diagnostic methods studied by Pregibon (1981, Ann. Statist. 9, 705-724), Cook and Weisberg (1982, Residuals and Influence in Regression, Chapman & Hall, New York), and Wei (1998, Exponential Family Nonlinear Models, Springer, Singapore) to nonlinear reproductive dispersion models (NRDM, Jorgensen, 1997, The Theory of Dispersion Models, Chapman & Hall, London). The equivalency of case-deletion models and mean-shift outlier models in NRDM is investigated. Some of the diagnostic measures are illustrated with an example.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:46:y:2000:i:1:p:59-68
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Xia, Tian & Wang, Yuebao, 2010. "A note on the properties of the reproductive dispersion model," Statistics & Probability Letters, Elsevier, vol. 80(17-18), pages 1397-1404, September.
    2. Vanegas, Luis Hernando & Cysneiros, Francisco José A., 2010. "Assessment of diagnostic procedures in symmetrical nonlinear regression models," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 1002-1016, April.
    3. Chen, Xue-Dong & Tang, Nian-Sheng, 2010. "Bayesian analysis of semiparametric reproductive dispersion mixed-effects models," Computational Statistics & Data Analysis, Elsevier, vol. 54(9), pages 2145-2158, September.
    4. Zhao Yuanying & Xu Dengke & Duan Xingde & Pang Yicheng, 2014. "Bayesian Subset Selection for Reproductive Dispersion Linear Models," Journal of Systems Science and Information, De Gruyter, vol. 2(1), pages 77-85, February.
    5. Tang, Nian-Sheng & Chen, Xing & Fu, Ying-Zi, 2009. "Bayesian analysis of non-linear structural equation models with non-ignorable missing outcomes from reproductive dispersion models," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 2031-2043, October.
    6. 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.
    7. Sun, Rui-Bo & Wei, Bo-Cheng, 2004. "On influence assessment for LAD regression," Statistics & Probability Letters, Elsevier, vol. 67(2), pages 97-110, April.
    8. Xia, Tian & Tang, Nian-Sheng & Wang, Xue-Ren, 2006. "Consistency and asymptotic normality of the maximum likelihood estimates in reproductive dispersion linear models," Statistics & Probability Letters, Elsevier, vol. 76(11), pages 1137-1146, June.
    9. 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.
    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. 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.

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