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Abstract:
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The varying-coefficient model (VCM) is a useful alternative to the additive models for determining the relationship between the covariates and a response, while accounting for interactions. In this article, we consider a functional framework for varying-coefficient models, where a scalar response is regressed on a scalar covariate and a functional covariate, taking the interaction between these covariates into account. Our primary interest is to test for the nullity of the effect of the interaction. We develop the likelihood ratio and the generalized F testing procedures in this framework. Performance of these testing procedures are investigated in a simulation study. We further demonstrate our testing procedures on a real data set.
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