Robust depth-based estimation of the functional autoregressive model

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

Robust depth-based estimation of the functional autoregressive model

Files

Martinez-Hernandez et al 2018 - Robust Depth-Based.pdf (707.26 KB)

Type

Article

Authors

Martinez Hernandez, Israel

Genton, Marc G.

González-Farías, Graciela

KAUST Department

Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Statistics Program

Online Publication Date

2018-06-14

Print Publication Date

2019-03

Date

2018-06-14

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.

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.