Functional Data Analysis (FDA) Including Regularized Regressions

Functional data analyis (FDA) analyzes data, that provide information of curves, and surfaces. Often, it is used to analyze, and predict times series data. Traditional analyses of time series are mostly based on multivariate analyses of variance, that completely ignore the effect of data smoothing, and suffer from power loss due to a positive correlation between the outcome variables. FDA uses smoothed curves for obtaining novel functions, that can be applied for making predictions in practice. And, so, FDA may look like traditional multivariate analysis, but it is more powerful, because results from smoothed data are the start of something new. FDA, if used as a data generating activity, will be pretty meaningless, and sound prior hypotheses are an essential background. In this chapter an example is given of an FDA procedure, including (1) data dimension reduction with principal components analysis, (2) optimal scaling of the reduced data with spline smoothing, (3) Ridge, Lasso, and Elastic Net regularization for increased precision. All of this is processed in a single analysis, and leads to a final analysis result with a better precision, than that of the Traditional regressions.