Regression analysis for a functional response
Technometrics
Estimation in generalized linear models for functional data via penalized likelihood
Journal of Multivariate Analysis
Editorial: Statistics for Functional Data
Computational Statistics & Data Analysis
Variational Bayesian functional PCA
Computational Statistics & Data Analysis
Additive prediction and boosting for functional data
Computational Statistics & Data Analysis
Structural components in functional data
Computational Statistics & Data Analysis
Measures of influence for the functional linear model with scalar response
Journal of Multivariate Analysis
Structural test in regression on functional variables
Journal of Multivariate Analysis
Computational Statistics & Data Analysis
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Methods of regression diagnostics for functional regression models are developed which relate a functional response to predictor variables that can be multivariate vectors or random functions. For this purpose, a residual process is defined by subtracting the predicted from the observed response functions. This residual process is expanded into functional principal components (FPC), and the corresponding FPC scores are used as natural proxies for the residuals in functional regression models. For the case of a univariate covariate, a randomization test is proposed 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 FPC 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 trajectories as well as functional data from a dose-response experiment for Mediterranean fruit flies (Ceratitis capitata).