Title: A minimax hypothesis test in smoothing spline ANOVA models
Authors: WenXuan Zhong - University of Georgia (United States) [presenting]
Abstract: Smoothing spline ANOVA (SSANOVA) model has been a popular choice for building the nonparametric regression model with multiple predictors. Extensive research efforts have been devoted to model fitting. However, testing the significance of components in SSANOVA is still lacking. We will present a test for testing the significance of the interaction in a bivariate SSANOVA model. We derive the limiting distribution of our test statistics which unveils a new version of Wilks phenomenon. We prove that the proposed test achieves the minimax rate for hypothesis testing. Simulation studies are conducted to investigate the empirical performance of the proposed test in the context. Application analysis offers numerical support to DNA methylation and neuroimaging studies.