Bernoulli

  • Bernoulli
  • Volume 24, Number 3 (2018), 2328-2357.

M-estimators of location for functional data

Beatriz Sinova, Gil González-Rodríguez, and Stefan Van Aelst

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Abstract

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.

Article information

Source
Bernoulli, Volume 24, Number 3 (2018), 2328-2357.

Dates
Received: February 2016
Revised: October 2016
First available in Project Euclid: 2 February 2018

Permanent link to this document
https://projecteuclid.org/euclid.bj/1517540476

Digital Object Identifier
doi:10.3150/17-BEJ929

Mathematical Reviews number (MathSciNet)
MR3757531

Zentralblatt MATH identifier
06839268

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

Citation

Sinova, Beatriz; González-Rodríguez, Gil; Van Aelst, Stefan. M-estimators of location for functional data. Bernoulli 24 (2018), no. 3, 2328--2357. doi:10.3150/17-BEJ929. https://projecteuclid.org/euclid.bj/1517540476


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