Wavelet-Based Scalar-on-Function Finite Mixture Regression Models

• Activity Number: 474
• Type: Topic Contributed
• Date/Time: Wednesday, August 7, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Adam Ciarleglio*+ and R. Todd Ogden
• Companies: Columbia University and Columbia University
• Keywords: EM algorithm ; Functional data analysis ; Lasso ; Wavelet regression

Abstract

Classical finite mixture regression is useful for modeling the relationships between scalar predictors and scalar responses arising from a heterogeneous population. Here we extend the classical finite mixture regression model to incorporate functional predictors by taking a wavelet-based approach in which we represent both the functional predictors and the component specific coefficient functions in terms of an appropriate wavelet basis. Using this representation, the wavelet coefficients corresponding to the functional covariate become the predictors. In this setting, we typically have many more predictors than observations. Hence we use a lasso-type penalization to perform variable selection and estimation. We also consider an adaptive version of our wavelet-based model. We discuss the specification of the model, provide a fitting algorithm, and apply and evaluate our methods using both simulations and a real data set.