TY - JOUR
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 -