Diagnostics for functional regression via residual processes
Computational Statistics & Data Analysis
Factor-based comparison of groups of curves
Computational Statistics & Data Analysis
Principal component analysis of measures, with special emphasis on grain-size curves
Computational Statistics & Data Analysis
Classifying densities using functional regression trees: Applications in oceanology
Computational Statistics & Data Analysis
Kalman filtering from POP-based diagonalization of ARH(1)
Computational Statistics & Data Analysis
Distance-based local linear regression for functional predictors
Computational Statistics & Data Analysis
Principal components for multivariate functional data
Computational Statistics & Data Analysis
Computational Statistics & Data Analysis
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Analyzing functional data often leads to finding common factors, for which functional principal component analysis proves to be a useful tool to summarize and characterize the random variation in a function space. The representation in terms of eigenfunctions is optimal in the sense of L"2 approximation. However, the eigenfunctions are not always directed towards an interesting and interpretable direction in the context of functional data and thus could obscure the underlying structure. To overcome such difficulty, an alternative to functional principal component analysis is proposed that produces directed components which may be more informative and easier to interpret. These structural components are similar to principal components, but are adapted to situations in which the domain of the function may be decomposed into disjoint intervals such that there is effectively independence between intervals and positive correlation within intervals. The approach is demonstrated with synthetic examples as well as real data. Properties for special cases are also studied.