BIRS Workshop Lecture Videos
Shape testing for coefficient functions in varying coefficient models Gijbels, Irene
Varying coefficient models are quite appealing for describing complex data structures. In this talk we consider varying coefficient models in the context of longitudinal data. The aim is to study possible qualitative properties of the unknown coefficient functions in the model. Among the qualitative properties that are of interest are: whether a coefficient function is constant or not; and whether it is a monotone function or not, or a convex function or not. Also simultaneous testing for qualitative properties of several coefficient functions is an important issue for applications. This problem of shape testing appears in different settings, such as mean regression and quantile regression, and in homoscedastic or heteroscedastic settings. We discuss shape constraint testing procedures under various settings, illustrate the performances of the procedures with some small simulation study, and demonstrate their use in real data analysis.
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