Inverse Regression for Multivariate Functional Data

• Activity Number: 616 - New Advances in Semiparametric Modeling and Testing for Complex Data
• Type: Topic Contributed
• Date/Time: Thursday, August 2, 2018 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Ci-Ren Jiang* and Lu-Hung Chen
• Companies: Academia Sinica and National Chung-Hsing University
• Keywords: Big Data; Multivariate Functional Data; Inverse Regression; Smoothing

Abstract

Inverse regression is an appearing dimension reduction method for regression models with multivariate covariates. Recently, it has been extended to the cases with functional or longitudinal covariates. However, the extensions simply focus on one single functional or longitudinal covariate. Motivated by a real application, we extend functional inverse regression to the cases with multiple functional covariates, whose domains could be different. The asymptotical properties of the proposed estimators are investigated for both functional and longitudinal cases. The computational issues are taken care with data binning, the fast Fourier transformation and random projections on a multi-core computation platform. In addition to simulation studies, the proposed approach is applied to predict the wind power capacity factor of the next day with the weather forecasts made today. Both demonstrate the good performance of our method.