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Jackknife-after-bootstrap regression influence diagnostics

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  • Michael Martin
  • Steven Roberts

Abstract

We propose a bootstrap approach to gauging the size of regression influence measures. The bootstrap cut-offs generated are based on approximating the sampling distribution of the respective measures under resampling, work well for small samples, and allow for features such as asymmetric cut-offs. The bootstrap method uses Efron's jackknife-after-bootstrap idea to deal with the issue of an influential point contaminating the resamples from which cut-offs are calculated. The method is illustrated through both real-world examples and a simulation study, the results of which suggest that the bootstrap method provides a reliable alternative to traditional methods particularly in small to moderate samples.

Suggested Citation

  • Michael Martin & Steven Roberts, 2010. "Jackknife-after-bootstrap regression influence diagnostics," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(2), pages 257-269.
    • Handle: RePEc:taf:gnstxx:v:22:y:2010:i:2:p:257-269
    DOI: 10.1080/10485250903287906
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    References listed on IDEAS

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    1. Wing‐Kam Fung & Zhong‐Yi Zhu & Bo‐Cheng Wei & Xuming He, 2002. "Influence diagnostics and outlier tests for semiparametric mixed models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 565-579, August.
    2. Michael Martin & Steven Roberts, 2006. "An evaluation of bootstrap methods for outlier detection in least squares regression," Journal of Applied Statistics, Taylor & Francis Journals, vol. 33(7), pages 703-720.
    3. Kim, Choongrak, 1996. "Cook's distance in spline smoothing," Statistics & Probability Letters, Elsevier, vol. 31(2), pages 139-144, December.
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    1. Ufuk Beyaztas & Aylin Alin, 2014. "Sufficient jackknife-after-bootstrap method for detection of influential observations in linear regression models," Statistical Papers, Springer, vol. 55(4), pages 1001-1018, November.
    2. Ufuk Beyaztas & Aylin Alin & Michael A. Martin, 2014. "Robust BCa-JaB method as a diagnostic tool for linear regression models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(7), pages 1593-1610, July.
    3. J. M. Muñoz-Pichardo & J. L. Moreno-Rebollo & R. Pino-Mejías & M. D. Cubiles Vega, 2019. "Influence measures in beta regression models through distance between distributions," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(2), pages 163-185, June.
    4. Ufuk Beyaztas & Beste H. Beyaztas, 2019. "On Jackknife-After-Bootstrap Method for Dependent Data," Computational Economics, Springer;Society for Computational Economics, vol. 53(4), pages 1613-1632, April.

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