Goodness-of-fit tests for functional linear models based on integrated projections

Functional linear models are one of the most fundamental tools to assess the relation between two random variables of a functional or scalar nature. This contribution proposes a goodness-of-fit test for the functional linear model with functional response that neatly adapts to functional/scalar responses/predictors. In particular, the new goodness-of-fit test extends a previous proposal for scalar response. The test statistic is based on a convenient regularized estimator, is easy to compute, and is calibrated through an efficient bootstrap resampling. A graphical diagnostic tool, useful to visualize the deviations from the model, is introduced and illustrated with a novel data application. The R package goffda implements the proposed methods and allows for the reproducibility of the data application.

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset