Global Test of Functional Effects in Mean Field Variational Bayesian Scalar-on-Function Regression
Abstract
Variational regression methods are increasingly popular because they enable efficient estimation in complex statistical models. To characterize their theoretical properties, researchers have established frequentist properties for models fitted using mean-field variational Bayes (MFVB). However, hypothesis testing in this framework remains understudied. We propose a global test for functional effects in scalar-on-function regression. The test combines consistency results for MFVB estimators with an existing test for smoothed semiparametric curves. To implement the procedure, we also develop a coordinate ascent variational inference (CAVI) algorithm for MFVB scalar-on-function regression, rather than relying on existing black-box procedures. Finally, we conduct a simulation study comparing our estimation procedure and global test with fully frequentist and fully Bayesian alternatives in terms of bias, root mean squared error, size, and power.