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On the Robustness and Sensitivity of Several Nonparametric Estimators via the Influence Curve Measure: A Brief Study

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  • Indranil Ghosh

    (Department of Mathematics and Statistics, University of North Carolina, Wilmington, NC 28403, USA)

  • Kathleen Fleming

    (Department of Mathematics and Statistics, University of North Carolina, Wilmington, NC 28403, USA)

Abstract

The use of influence curve as a measure of sensitivity is not new in the literature but has not been properly explored to the best of our knowledge. In particular, the mathematical derivation of the influence function for several popular nonparametric estimators (such as trimmed mean, α -winsorized mean, Pearson product moment correlation coefficient etc. among notable ones) is not given in adequate detail. Moreover, the summary of the final expressions given in some sporadic cases does not appear to be correct. In this article, we aim to examine and summarize the derivation of the influence curve for various well-known estimators for estimating the location of a population, many of which are considered in the nonparametric paradigm.

Suggested Citation

  • Indranil Ghosh & Kathleen Fleming, 2022. "On the Robustness and Sensitivity of Several Nonparametric Estimators via the Influence Curve Measure: A Brief Study," Mathematics, MDPI, vol. 10(17), pages 1-16, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:17:p:3100-:d:900511
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    References listed on IDEAS

    as
    1. Mingxin Wu & Yijun Zuo, 2008. "Trimmed and winsorized standard deviations based on a scaled deviation," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(4), pages 319-335.
    2. Hongtu Zhu & Joseph G. Ibrahim & Niansheng Tang, 2011. "Bayesian influence analysis: a geometric approach," Biometrika, Biometrika Trust, vol. 98(2), pages 307-323.
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