Simultaneous confidence bands for functional regression models

- A general function-on-scalar regression model is considered.
- This model allows multiple covariates and heterogeneity.
- A wild bootstrap method is proposed to estimate SCBs for the coefficient function.
- Some asymptotic results are provided.

In recent years, the field of functional data analysis (FDA) has received a great deal of attention, and many useful theories and interesting applications have been reported. One topic of particular interest involves estimation of simultaneous confidence bands (SCB) for an unknown function. Degras (2011) proposed an estimator of SCBs for the mean function in a simple (no covariates) function-on-scalar regression model that relies on some assumptions on the tail behavior of the errors. In the case that such distributional assumptions do not hold, Degras also proposed a bootstrap method (sampling with replacement). We consider a more general function-on-scalar regression model that involves multiple covariates and allows the variance function of the functional responses to be dependent on the covariates (heterogeneity). In this general model, we propose a wild bootstrap method for estimating SCBs for the coefficient function. Some asymptotic results are provided for the simple case (no covariates) and simulation results for both the simple and general models.