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Variable selection in nonlinear function-on-scalar regression
Authors:Rahul Ghosal  Arnab Maity
Institution:1. Department of Biostatistics, Johns Hopkins Bloomberg School of Public Health, Baltimore, Maryland;2. Department of Statistics, North Carolina State University, Raleigh, North Carolina
Abstract:We develop a new method for variable selection in a nonlinear additive function-on-scalar regression (FOSR) model. Existing methods for variable selection in FOSR have focused on the linear effects of scalar predictors, which can be a restrictive assumption in the presence of multiple continuously measured covariates. We propose a computationally efficient approach for variable selection in existing linear FOSR using functional principal component scores of the functional response and extend this framework to a nonlinear additive function-on-scalar model. The proposed method provides a unified and flexible framework for variable selection in FOSR, allowing nonlinear effects of the covariates. Numerical analysis using simulation study illustrates the advantages of the proposed method over existing variable selection methods in FOSR even when the underlying covariate effects are all linear. The proposed procedure is demonstrated on accelerometer data from the 2003–2004 cohorts of the National Health and Nutrition Examination Survey (NHANES) in understanding the association between diurnal patterns of physical activity and demographic, lifestyle, and health characteristics of the participants.
Keywords:functional data analysis  functional principal component analysis  function-on-scalar regression  NHANES  nonlinear regression  variable selection
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