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Robust BCa-JaB method as a diagnostic tool for linear regression models

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  • Ufuk Beyaztas
  • Aylin Alin
  • Michael A. Martin

Abstract

The Jackknife-after-bootstrap (JaB) technique originally developed by Efron [8] has been proposed as an approach to improve the detection of influential observations in linear regression models by Martin and Roberts [12] and Beyaztas and Alin [2]. The method is based on the use of percentile-method confidence intervals to provide improved cut-off values for several single case-deletion influence measures. In order to improve JaB, we propose using robust versions of Efron [7]'s bias-corrected and accelerated (BCa) bootstrap confidence intervals. In this study, the performances of robust BCa-JaB and conventional JaB methods are compared in the cases of DFFITS, Welsch's distance and modified Cook's distance influence diagnostics. Comparisons are based on both real data examples and through a simulation study. Our results reveal that under a variety of scenarios, our proposed method provides more accurate and reliable results, and it is more robust to masking effects.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:japsta:v:41:y:2014:i:7:p:1593-1610
    DOI: 10.1080/02664763.2014.881788
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    1. Michael Martin & Steven Roberts, 2010. "Jackknife-after-bootstrap regression influence diagnostics," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(2), pages 257-269.
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    1. 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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