Robust depth-based estimation of the functional autoregressive model

Israel Martinez Hernandez; Marc G. Genton; Graciela González-Farías

doi:10.1016/j.csda.2018.06.003

Robust depth-based estimation of the functional autoregressive model

Israel Martinez Hernandez, Marc G. Genton, Graciela González-Farías

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

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.

Original language	English (US)
Pages (from-to)	66-79
Number of pages	14
Journal	Computational Statistics & Data Analysis
Volume	131
DOIs	https://doi.org/10.1016/j.csda.2018.06.003
State	Published - Jun 14 2018

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: 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.

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10.1016/j.csda.2018.06.003

https://repository.kaust.edu.sa/bitstream/10754/628526/1/Martinez-Hernandez%20et%20al%202018%20-%20Robust%20Depth-Based.pdf

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@article{3ae1ee2499074546a685e6b135f8083f,

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 CO concentrations in California.",

author = "{Martinez Hernandez}, Israel and Genton, {Marc G.} and Graciela Gonz{\'a}lez-Far{\'i}as",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: This research was partially supported by (1) CONACYT, M{\'e}xico, scholarship as visiting research student, (2) CONACYT, M{\'e}xico, 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.",

year = "2018",

month = jun,

day = "14",

doi = "10.1016/j.csda.2018.06.003",

language = "English (US)",

volume = "131",

pages = "66--79",

journal = "Computational Statistics & Data Analysis",

issn = "0167-9473",

publisher = "Elsevier",

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

AU - Martinez Hernandez, Israel

AU - Genton, Marc G.

AU - González-Farías, Graciela

N1 - KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: 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.

PY - 2018/6/14

Y1 - 2018/6/14

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 CO 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 CO concentrations in California.

UR - http://hdl.handle.net/10754/628526

UR - http://www.sciencedirect.com/science/article/pii/S0167947318301415

UR - http://www.scopus.com/inward/record.url?scp=85048927976&partnerID=8YFLogxK

U2 - 10.1016/j.csda.2018.06.003

DO - 10.1016/j.csda.2018.06.003

M3 - Article

SN - 0167-9473

VL - 131

SP - 66

EP - 79

JO - Computational Statistics & Data Analysis

JF - Computational Statistics & Data Analysis

ER -

Robust depth-based estimation of the functional autoregressive model

Abstract

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