Open Access
August 2018 M-estimators of location for functional data
Beatriz Sinova, Gil González-Rodríguez, Stefan Van Aelst
Bernoulli 24(3): 2328-2357 (August 2018). DOI: 10.3150/17-BEJ929


M-estimators of location are widely used robust estimators of the center of univariate or multivariate real-valued data. This paper aims to study M-estimates of location in the framework of functional data analysis. To this end, recent developments for robust nonparametric density estimation by means of M-estimators are considered. These results can also be applied in the context of functional data analysis and allow to state conditions for the existence and uniqueness of location M-estimates in this setting. Properties of these functional M-estimators are investigated. In particular, their consistency is shown and robustness is studied by means of their breakdown point and their influence function. The finite-sample performance of the M-estimators is explored by simulation. The M-estimators are also empirically compared to trimmed means for functional data.


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Beatriz Sinova. Gil González-Rodríguez. Stefan Van Aelst. "M-estimators of location for functional data." Bernoulli 24 (3) 2328 - 2357, August 2018.


Received: 1 February 2016; Revised: 1 October 2016; Published: August 2018
First available in Project Euclid: 2 February 2018

zbMATH: 06839268
MathSciNet: MR3757531
Digital Object Identifier: 10.3150/17-BEJ929

Keywords: functional data , functional data metric , Hampel loss , Huber loss , M-estimates of location , statistical robustness , Trimmed means , Tukey loss

Rights: Copyright © 2018 Bernoulli Society for Mathematical Statistics and Probability

Vol.24 • No. 3 • August 2018
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