Univariate splines and their tensor products will be used to construct approximations to infinite-dimensional main effect and interaction components for models of unknown (exponential family) distributions or conditional distributions. Theoretical properties will be explored in mathematically rigorous fashion and real examples will be pursued for data assumed to come from independent trials and for data from bivariate time series. The overall goal is to improve the efficacy and accessibility of the statistical framework underlying the analysis of data and the design of experiments.
