Robust Estimation of a Location Parameter with the Integrated Hogg Function

15 Pages Posted: 13 Jan 2020

See all articles by Leopoldo Catania

Leopoldo Catania

Aarhus University - School of Business and Social Sciences; Aarhus University - CREATES

Alessandra Luati

University of Bologna - Department of Statistics

Date Written: December 17, 2019

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.

Keywords: Robust statistics, Hogg function, M-estimator

Suggested Citation

Catania, Leopoldo and Luati, Alessandra, Robust Estimation of a Location Parameter with the Integrated Hogg Function (December 17, 2019). Available at SSRN: https://ssrn.com/abstract=3507948 or http://dx.doi.org/10.2139/ssrn.3507948

Leopoldo Catania (Contact Author)

Aarhus University - School of Business and Social Sciences ( email )

Fuglesangs Allé 4
Aarhus V, DK-8210
Denmark
+4587165536 (Phone)

HOME PAGE: http://pure.au.dk/portal/en/leopoldo.catania@econ.au.dk

Aarhus University - CREATES ( email )

School of Economics and Management
Building 1322, Bartholins Alle 10
DK-8000 Aarhus C
Denmark

Alessandra Luati

University of Bologna - Department of Statistics ( email )

Bologna, 40126
Italy

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