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Robust depth-based estimation of the functional autoregressive model

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Robust depth-based estimation of the functional autoregressive model. / Martínez-Hernández, Israel; Genton, Marc G.; González-Farías, Graciela.
In: Computational Statistics and Data Analysis, Vol. 131, 31.03.2019, p. 66-79.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Martínez-Hernández, I, Genton, MG & González-Farías, G 2019, 'Robust depth-based estimation of the functional autoregressive model', Computational Statistics and Data Analysis, vol. 131, pp. 66-79. https://doi.org/10.1016/j.csda.2018.06.003

APA

Martínez-Hernández, I., Genton, M. G., & González-Farías, G. (2019). Robust depth-based estimation of the functional autoregressive model. Computational Statistics and Data Analysis, 131, 66-79. https://doi.org/10.1016/j.csda.2018.06.003

Vancouver

Martínez-Hernández I, Genton MG, González-Farías G. Robust depth-based estimation of the functional autoregressive model. Computational Statistics and Data Analysis. 2019 Mar 31;131:66-79. Epub 2018 Jun 14. doi: 10.1016/j.csda.2018.06.003

Author

Martínez-Hernández, Israel ; Genton, Marc G. ; González-Farías, Graciela. / Robust depth-based estimation of the functional autoregressive model. In: Computational Statistics and Data Analysis. 2019 ; Vol. 131. pp. 66-79.

Bibtex

@article{71bb3ebc74274e969e0aa23dcac8c9e2,
title = "Robust depth-based estimation of the functional autoregressive model",
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 CO2 concentrations in California.",
keywords = "Functional autoregression model, Functional data analysis, Functional regression model, Functional time series, Influence function, Robust estimator",
author = "Israel Mart{\'i}nez-Hern{\'a}ndez and Genton, {Marc G.} and Graciela Gonz{\'a}lez-Far{\'i}as",
note = "High-dimensional and functional data analysis",
year = "2019",
month = mar,
day = "31",
doi = "10.1016/j.csda.2018.06.003",
language = "English",
volume = "131",
pages = "66--79",
journal = "Computational Statistics and Data Analysis",
issn = "0167-9473",
publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - Robust depth-based estimation of the functional autoregressive model

AU - Martínez-Hernández, Israel

AU - Genton, Marc G.

AU - González-Farías, Graciela

N1 - High-dimensional and functional data analysis

PY - 2019/3/31

Y1 - 2019/3/31

N2 - 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 CO2 concentrations in California.

AB - 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 CO2 concentrations in California.

KW - Functional autoregression model

KW - Functional data analysis

KW - Functional regression model

KW - Functional time series

KW - Influence function

KW - Robust estimator

U2 - 10.1016/j.csda.2018.06.003

DO - 10.1016/j.csda.2018.06.003

M3 - Journal article

VL - 131

SP - 66

EP - 79

JO - Computational Statistics and Data Analysis

JF - Computational Statistics and Data Analysis

SN - 0167-9473

ER -