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    Robust depth-based estimation of the functional autoregressive model

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    Martinez-Hernandez et al 2018 - Robust Depth-Based.pdf
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    Type
    Article
    Authors
    Martinez Hernandez, Israel cc
    Genton, Marc G. cc
    González-Farías, Graciela
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Statistics Program
    Date
    2018-06-14
    Online Publication Date
    2018-06-14
    Print Publication Date
    2019-03
    Permanent link to this record
    http://hdl.handle.net/10754/628526
    
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    Abstract
    A robust estimator for functional autoregressive models is proposed, the Depth-based Least Squares (DLS) estimator. The DLS estimator down-weights the influence of outliers by using the functional directional outlyingness as a centrality measure. It consists of two steps: identifying the outliers with a two-stage functional boxplot, then down-weighting the outliers using the functional directional outlyingness. Theoretical properties of the DLS estimator are investigated such as consistency and boundedness of its influence function. Through a Monte Carlo study, it is shown that the DLS estimator performs better than estimators based on Principal Component Analysis (PCA) and robust PCA, which are the most commonly used. To illustrate a practical application, the DLS estimator is used to analyze a dataset of ambient CO concentrations in California.
    Citation
    Martínez-Hernández I, Genton MG, González-Farías G (2018) Robust depth-based estimation of the functional autoregressive model. Computational Statistics & Data Analysis. Available: http://dx.doi.org/10.1016/j.csda.2018.06.003.
    Sponsors
    This research was partially supported by (1) CONACYT, México, scholarship as visiting research student, (2) CONACYT, México, CB-2015-01-252996, and (3) King Abdullah University of Science and Technology (KAUST). The authors thank the two anonymous referees for their valuable comments.
    Publisher
    Elsevier BV
    Journal
    Computational Statistics & Data Analysis
    DOI
    10.1016/j.csda.2018.06.003
    Additional Links
    http://www.sciencedirect.com/science/article/pii/S0167947318301415
    ae974a485f413a2113503eed53cd6c53
    10.1016/j.csda.2018.06.003
    Scopus Count
    Collections
    Articles; Statistics Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

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