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Diagnostic procedures in Birnbaum–Saunders nonlinear regression models

Listed author(s):
  • Vanegas, Luis Hernando
  • Rondón, Luz Marina
  • Cysneiros, Francisco José A.
Registered author(s):

    This paper proposes a general definition of residuals for Birnbaum–Saunders nonlinear regression models by studying their statistical properties analytically and using Monte Carlo experiments. Also, some diagnostic procedures are derived based on case-deletion and mean-shift outlier models such as one-step approximation, likelihood displacement, generalized Cook’s distance, outlier tests and some measures for identifying influential observations on partial F-test. A test for homogeneity of shape parameter is also developed. Residuals and influence diagnostic tools are illustrated by means of an example that allows us to relate the response variable lifetime of a metal piece and the explanatory variable work per cycle. Three models were compared to fit the dataset, two of them with nonlinear systematic components.

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    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 56 (2012)
    Issue (Month): 6 ()
    Pages: 1662-1680

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    Handle: RePEc:eee:csdana:v:56:y:2012:i:6:p:1662-1680
    DOI: 10.1016/j.csda.2011.10.008
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    1. 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.
    2. Bo-Cheng Wei & Jian-Qing Shi & Wing-Kam Fung & Yue-Qing Hu, 1998. "Testing for Varying Dispersion in Exponential Family Nonlinear Models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(2), pages 277-294, June.
    3. Wei, Wen Hsiang & Fung, Wing Kam, 1999. "The mean-shift outlier model in general weighted regression and its applications," Computational Statistics & Data Analysis, Elsevier, vol. 30(4), pages 429-441, June.
    4. 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.
    5. 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.
    6. 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.
    7. Lemonte, Artur J. & Cordeiro, Gauss M., 2009. "Birnbaum-Saunders nonlinear regression models," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4441-4452, October.
    8. 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.
    9. Xie, Feng-Chang & Wei, Bo-Cheng & Lin, Jin-Guan, 2009. "Homogeneity diagnostics for skew-normal nonlinear regression models," Statistics & Probability Letters, Elsevier, vol. 79(6), pages 821-827, March.
    10. Sun, Rui-Bo & Wei, Bo-Cheng, 2004. "On influence assessment for LAD regression," Statistics & Probability Letters, Elsevier, vol. 67(2), pages 97-110, April.
    11. Cysneiros, Francisco José A. & Vanegas, Luis Hernando, 2008. "Residuals and their statistical properties in symmetrical nonlinear models," Statistics & Probability Letters, Elsevier, vol. 78(18), pages 3269-3273, December.
    12. 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.
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