Robust Estimation for the Function-on-Function Regression Model

• Activity Number: 390 - Functional and High-Dimensional Data
• Type: Contributed
• Date/Time: Wednesday, August 10, 2022 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Ufuk Beyaztas and Han Lin Shang and Abhijit Mandal*
• Companies: Marmara University and Macquarie University and Univeristy of Texas at El Paso
• Keywords: non-linear regression; robust estimation; function-on-function regression model; tau-estimator; functional principal component analysis

Abstract

We propose a robust estimation strategy to estimate the function-on-function regression model that is stable against large outliers in the response variable. The approach is based on the robust functional principal component analysis (PCA) and the tau-estimator. The performance of the proposed method relies on the truncation parameters of the robust functional PCA. Thus, a robust Bayesian information criterion is used to determine the optimum truncation parameters. Furthermore, a forward stepwise variable selection procedure is employed to determine significant main, quadratic, and interaction effects. In addition, the asymptotic consistency and influence function of the proposed method are investigated. Finally, the empirical performance of the proposed method is evaluated through a series of Monte Carlo simulations and the U.S. COVID-19 dataset.