Abstract: Motivated by applications, we propose a class of dynamic single-index varying-coefficient models to explore the varying interaction effects on the response variable among a set of covariates. That is, the interaction effects are allowed to change with some factors of interest, such as time, spatial location, or other covariates. A spline-based approach is developed to estimate the index and varying-coefficient functions. The convergence rates and asymptotic normalities of the resulting estimators are established. It is also shown that the resulting estimators exhibit the oracle property. A penalized method is presented to select related covariates, and the consistency of the penalized estimator is proved. A test statistic is provided to check whether the interaction effect also varies with the factors of interest, and the asymptotic normality of the test statistic is established. Simulation studies and two real-data analyses illustrate the good performance of the proposed model and the corresponding statistical inference methods for finite samples.

Key words and phrases: Interaction effect, single-index varying-coefficient regression model, spline approximation, variable selection.