Most-Predictive Domain Selection for Functional Linear Regression

• Activity Number: 355
• Type: Contributed
• Date/Time: Tuesday, August 11, 2015 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Ah Yeon Park* and John Aston and Frédéric Ferraty
• Companies: University of Cambridge and University of Cambridge and Institut de Mathématiques de Toulouse
• Keywords: domain selection for functional predictor ; functional linear regression ; nonparametric variable selection ; segmentation of functional data ; sequential algorithm

Abstract

We introduce an algorithm which, in the context of functional linear regression, selects the domain of a functional predictor, X, that optimizes the prediction of a scalar response, Y. This new approach is particularly beneficial when the regression coefficient is known to have localized features, and can facilitate interpretation. The methodology involves two estimation steps. First, we segment the integral domain into several parts, depending on the correlation structure of the predictor. This amounts to minimizing a stepwise loss function, in which a new location giving the optimal segmentation is added at each step. The second estimation step is the selection of the optimal combination of segments, based on a cross-validated error criterion. It involves a sequential algorithm that extends the type of possible combinations of segments retained at each step, while keeping the computational burden in a reasonable range. The algorithm is terminated when the difference between two successive mean squared error of Y falls below a given level. We illustrate the effectiveness of our methodology through simulations in a range of settings. Also, we explore the theoretical properties.