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Robust estimation of a location parameter with the integrated Hogg function

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  • Catania, Leopoldo
  • Luati, Alessandra

Abstract

We study the properties of an M-estimator arising from the minimization of an integrated version of the quantile loss function. The estimator depends on a tuning parameter which controls the degree of robustness. We show that the sample median and the sample mean are obtained as limit cases. Consistency and asymptotic normality are established and a link with the Hodges–Lehmann estimator and the Wilcoxon test is discussed. Asymptotic results indicate that high levels of efficiency can be reached by specific choices of the tuning parameter. A Monte Carlo analysis investigates the finite sample properties of the estimator. Results indicate that efficiency can be preserved in finite samples by setting the tuning parameter to a low fraction of a (robust) estimate of the scale.

Suggested Citation

  • Catania, Leopoldo & Luati, Alessandra, 2020. "Robust estimation of a location parameter with the integrated Hogg function," Statistics & Probability Letters, Elsevier, vol. 164(C).
    • Handle: RePEc:eee:stapro:v:164:y:2020:i:c:s0167715220301152
    DOI: 10.1016/j.spl.2020.108812
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    References listed on IDEAS

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