Diagnostics for functional regression via residual processes

We develop regression diagnostics for functional regression models which relate a functional response to predictor variables that can be multivariate vectors or random functions. For this purpose, we define a residual process by subtracting the predicted from the observed response functions. This residual process is expanded into functional principal components, and the corresponding functional principal component scores are used as natural proxies for the residuals in functional regression models. For the case of a univariate covariate, we propose a randomization test based on these scores to examine if the residual process depends on the covariate. If this is the case, it indicates lack of fit of the model. Graphical methods based on the functional principal component scores of observed and fitted functions can be used to complement more formal tests. The methods are illustrated with data from a recent study of Drosophila fruit flies regarding life-cycle gene expression trajecto...

• Type: Journal
• Year: 2007
• Where: CSDA
• Authors: Jeng-Min Chiou, Hans-Georg Müller
• Keywords: CSDA 2007, Functional Principal Component, Functional Regression Models, Residual Process