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Pointwise influence matrices for functional-response regression
Biometrics (2017)
  • Philip T. Reiss
  • Lei Huang
  • Pei-Shien Wu
  • Huaihou Chen
  • Stan Colcombe
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 hat 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. 

Keywords
  • Bivariate smoothing,
  • Degrees of freedom,
  • Fractional anisotropy,
  • Function-on-scalar regression,
  • Functional nonlinear regression,
  • Neurodevelopmental trajectory,
  • Tensor product spline
Publication Date
2017
Citation Information
Philip T. Reiss, Lei Huang, Pei-Shien Wu, Huaihou Chen, et al.. "Pointwise influence matrices for functional-response regression" Biometrics Vol. in press (2017)
Available at: http://works.bepress.com/phil_reiss/43/