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A diagnostic procedure based on local influence

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  • Hongtu Zhu

Abstract

Cook's (1986) normal curvature measure is useful for sensitivity analysis of model assumptions in statistical models. However, there is no rigorous approach based on the normal curvature for addressing two fundamental issues: to assess the extent of discrepancy between an assumed model and the underlying model from which the data are generated, and to identify suspicious data points for which the discrepancy is most evident. Our purpose is to establish a theoretically sound procedure for resolving these issues for case-weight perturbation under the framework of independent distributions. We show that the local influence measure, Cook's distance and likelihood distance are asymptotically equivalent. A diagnostic procedure, based on local influence, is proposed for evaluating model misspecification and for detecting influential points simultaneously. We analyse two real datasets. Copyright Biometrika Trust 2004, Oxford University Press.

Suggested Citation

  • Hongtu Zhu, 2004. "A diagnostic procedure based on local influence," Biometrika, Biometrika Trust, vol. 91(3), pages 579-589, September.
    • Handle: RePEc:oup:biomet:v:91:y:2004:i:3:p:579-589
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    Cited by:

    1. Michelli Barros & Manuel Galea & Víctor Leiva & Manoel Santos-Neto, 2018. "Generalized Tobit models: diagnostics and application in econometrics," Journal of Applied Statistics, Taylor & Francis Journals, vol. 45(1), pages 145-167, January.
    2. Mário Fernando De Sousa & Helton Saulo & Víctor Leiva & Paulo Scalco, 2018. "On Some Properties Of A New Asymmetry-Based Tobit Model," Anais do XLIV Encontro Nacional de Economia [Proceedings of the 44th Brazilian Economics Meeting] 129, ANPEC - Associação Nacional dos Centros de Pós-Graduação em Economia [Brazilian Association of Graduate Programs in Economics].
    3. Bao Yiqi & Cibele Maria Russo & Vicente G. Cancho & Francisco Louzada, 2016. "Influence diagnostics for the Weibull-Negative-Binomial regression model with cure rate under latent failure causes," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(6), pages 1027-1060, May.
    4. 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.
    5. Edwin M.M. Ortega & Gauss M. Cordeiro & Michael W. Kattan, 2012. "The negative binomial--beta Weibull regression model to predict the cure of prostate cancer," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(6), pages 1191-1210, November.
    6. Chengcheng Hao & Dietrich Rosen & Tatjana Rosen, 2014. "Local Influence Analysis in AB–BA Crossover Designs," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(4), pages 1153-1166, December.
    7. Elizabeth Hashimoto & Gauss Cordeiro & Edwin Ortega, 2013. "The new Neyman type A beta Weibull model with long-term survivors," Computational Statistics, Springer, vol. 28(3), pages 933-954, June.
    8. Huang, Yufen & Kuo, Mei-Ling & Wang, Tai-Ho, 2007. "Pair-perturbation influence functions and local influence in PCA," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5886-5899, August.
    9. Espinheira, Patri­cia L. & Ferrari, Silvia L.P. & Cribari-Neto, Francisco, 2008. "Influence diagnostics in beta regression," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4417-4431, May.
    10. Hattori, Satoshi & Kato, Mai, 2009. "Approximate subject-deletion influence diagnostics for Inverse Probability of Censoring Weighted (IPCW) method," Statistics & Probability Letters, Elsevier, vol. 79(17), pages 1833-1838, September.
    11. V�ctor Leiva & Emilia Athayde & Cecilia Azevedo & Carolina Marchant, 2011. "Modeling wind energy flux by a Birnbaum--Saunders distribution with an unknown shift parameter," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(12), pages 2819-2838, February.

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