Robust Depth-Based Estimation of the Functional Autoregressive Model

• Activity Number: 304 - Clustering and Regression Analyzes
• Type: Contributed
• Date/Time: Tuesday, July 31, 2018 : 8:30 AM to 10:20 AM
• Sponsor: International Statistical Institute
• Author(s): Israel Martinez Hernandez* and Marc G Genton and Graciela Gonzalez Farias
• Companies: KAUST and King Abdullah University of Science and Technology and CIMAT
• Keywords: Functional autoregression model; Functional data analysis; Functional regression model; Functional time series; Influence function; Robust estimator

Abstract

We propose a robust estimator for functional autoregressive models. Our estimator, the Depth-based Least Squares (DLS) estimator, down-weights the influence of outliers by using the functional outlyingness as a centrality measure. The DLS estimator consists of two steps: identifying the outliers with a functional boxplot based on a defined depth, then down-weighting the outliers using the functional outlyingness. We prove that the influence function of the DLS estimator is bounded. Through a Monte Carlo study, we show that the DLS estimator performs better than the PCA and robust PCA estimators, which are the most commonly used.