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Activity Number: 245 - Methods for Analysis of High-Dimensional Data
Type: Contributed
Date/Time: Monday, July 30, 2018 : 2:00 PM to 3:50 PM
Sponsor: SSC
Abstract #330727
Title: Sparse Functional Additive Models
Author(s): Peijun Sang* and Liangliang Wang and Jiguo Cao
Companies: Simon Fraser University and Simon Fraser University and Simon Fraser University
Keywords: Functional Data Analysis;; Functional Linear Model; Functional Principal Component Analysis; Group LASSO; Regression Spline

We propose a new, more flexible model to tackle the issue of lack of fit for conventional functional linear regression. This new model, called the sparse functional additive model, is used to characterize the relationship between a functional predictor and a scalar response of interest. The effect of the functional predictor is represented in a nonparametric additive form, where the arguments are the scaled functional principal component scores. Component selection and smoothing are considered when tting the model to reduce the variability and enhance the prediction accuracy, while providing an adequate fit.

To achieve these goals, we propose using the adaptive group LASSO method to select relevant components and smoothing splines to obtain a smoothed estimate of those relevant components. Simulation studies show that the proposed estimation method compares favourably with various conventional methods in terms of prediction accuracy and component selection. The advantage of our proposed model and the estimation method is further demonstrated in two real data examples.

Authors who are presenting talks have a * after their name.

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