Adam Ciarleglio
Department of Biostatistics
Mailman School of Public Health
Columbia University
Monday, March 18, 2013, RI-224

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

Abstract: Classical finite mixture regression is useful for modeling the relationship between scalar predictors and scalar responses arising from subpopulations defined by the differing associations between those predictors and responses. 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. In the wavelet representation of the model, the wavelet coefficients corresponding to the functional data 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 discuss the specification of the model, provide a fitting algorithm, and apply and evaluate our wavelet-based method using both simulations and a real data set.