Abstract
We extend the notion of an influence or hat matrix to regression with functional responses and scalar predictors. For responses depending linearly on a set of predictors, our definition is shown to reduce to the conventional influence matrix for linear models. The pointwise degrees of freedom, the trace of the pointwise influence matrix, are shown to have an adaptivity property that motivates a two-step bivariate smoother for modeling nonlinear dependence on a single predictor. This procedure adapts to varying complexity of the nonlinear model at different locations along the function, and thereby achieves better performance than competing tensor product smoothers in an analysis of the development of white matter microstructure in the brain.
Original language | English |
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Pages (from-to) | 1092-1101 |
Number of pages | 10 |
Journal | Biometrics |
Volume | 73 |
Issue number | 4 |
DOIs | |
State | Published - 2017 |
Bibliographical note
Publisher Copyright:© 2017, The International Biometric Society
Keywords
- Bivariate smoothing
- Degrees of freedom
- Fractional anisotropy
- Function-on-scalar regression
- Functional nonlinear regression
- Neurodevelopmental trajectory
- Tensor product spline
ASJC Scopus subject areas
- Statistics and Probability
- General Biochemistry, Genetics and Molecular Biology
- General Immunology and Microbiology
- General Agricultural and Biological Sciences
- Applied Mathematics