Department of Economics and Business Economics

Robust Estimation of a Location Parameter with the Integrated Hogg Function

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Robust Estimation of a Location Parameter with the Integrated Hogg Function. / Catania, Leopoldo; Luati, Alessandra.

In: Statistics & Probability Letters, Vol. 164, 108812, 09.2020.

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Catania, Leopoldo ; Luati, Alessandra. / Robust Estimation of a Location Parameter with the Integrated Hogg Function. In: Statistics & Probability Letters. 2020 ; Vol. 164.

Bibtex

@article{c0041462172745a08e971eedf77c4d58,
title = "Robust Estimation of a Location Parameter with the Integrated Hogg Function",
abstract = "We study the properties of an M-estimator arising from the minimisation 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.",
author = "Leopoldo Catania and Alessandra Luati",
year = "2020",
month = sep,
doi = "10.1016/j.spl.2020.108812",
language = "English",
volume = "164",
journal = "Statistics & Probability Letters",
issn = "0167-7152",
publisher = "Elsevier BV * North-Holland",

}

RIS

TY - JOUR

T1 - Robust Estimation of a Location Parameter with the Integrated Hogg Function

AU - Catania, Leopoldo

AU - Luati, Alessandra

PY - 2020/9

Y1 - 2020/9

N2 - We study the properties of an M-estimator arising from the minimisation 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.

AB - We study the properties of an M-estimator arising from the minimisation 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.

U2 - 10.1016/j.spl.2020.108812

DO - 10.1016/j.spl.2020.108812

M3 - Journal article

VL - 164

JO - Statistics & Probability Letters

JF - Statistics & Probability Letters

SN - 0167-7152

M1 - 108812

ER -