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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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    1. James E. Matheson & Robert L. Winkler, 1976. "Scoring Rules for Continuous Probability Distributions," Management Science, INFORMS, vol. 22(10), pages 1087-1096, June.
    2. Bo Kai & Runze Li & Hui Zou, 2010. "Local composite quantile regression smoothing: an efficient and safe alternative to local polynomial regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(1), pages 49-69, January.
    3. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731, January.
    4. Tilmann Gneiting & Roopesh Ranjan, 2011. "Comparing Density Forecasts Using Threshold- and Quantile-Weighted Scoring Rules," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(3), pages 411-422, July.
    5. Takafumi Kanamori & Hironori Fujisawa, 2015. "Robust estimation under heavy contamination using unnormalized models," Biometrika, Biometrika Trust, vol. 102(3), pages 559-572.
    6. A. Philip Dawid & Monica Musio & Laura Ventura, 2016. "Minimum Scoring Rule Inference," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(1), pages 123-138, March.
    7. Koenker, Roger, 1984. "A note on L-estimates for linear models," Statistics & Probability Letters, Elsevier, vol. 2(6), pages 323-325, December.
    8. Gneiting, Tilmann & Raftery, Adrian E., 2007. "Strictly Proper Scoring Rules, Prediction, and Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 359-378, March.
    9. Gneiting, Tilmann & Ranjan, Roopesh, 2011. "Comparing Density Forecasts Using Threshold- and Quantile-Weighted Scoring Rules," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(3), pages 411-422.
    10. Davide Ferrari & Davide La Vecchia, 2012. "On robust estimation via pseudo-additive information," Biometrika, Biometrika Trust, vol. 99(1), pages 238-244.
    11. J. Pfanzagl, 1969. "On the measurability and consistency of minimum contrast estimates," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 14(1), pages 249-272, December.
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