Robust estimation of a location parameter with the integrated Hogg function

Leopoldo Catania and Alessandra Luati

Statistics & Probability Letters, 2020, vol. 164, issue C

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.

Keywords: M-estimators; Scoring rules; Quantile function; Robustness (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1016/j.spl.2020.108812

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