The UNLV Department of Mathematical Sciences invites you to a statistics seminar by assistant professor of statistics Youngjin Cho, Ph.D.
The seminar will take place Friday, Sept. 25, from 11:30 a.m. to 12:30 p.m. in Hospitality Hall, Room 380.
Title: Effect-Wise Inference for Smoothing Spline ANOVA on Tensor-Product Sobolev Space
Abstract: Functional ANOVA provides a flexible nonparametric framework for modeling multivariate covariates through interpretable main and interaction effect functions, but effect-wise inference remains challenging. Existing methods target inference for entire functions or suffer from key limitations: inability to accommodate interactions, lack of rigorous theory, or restriction to pointwise inference. To address these limitations, we develop a unified framework for effect-wise inference in smoothing spline ANOVA on a tensor-product Sobolev space, establishing convergence rates, pointwise confidence intervals, and Wald-type tests for detecting nonzero effects. Main effects achieve the optimal univariate rates, and interactions achieve optimal rates up to logarithmic factors. The theory relies on an orthogonal decomposition of effect subspaces, enabling functional Bahadur representation for effect-wise inference. Simulations and real-data applications show superior performance over existing methods.
