Derivative estimation and testing in generalized additive models |
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| Institution: | 1. National Intrepid Center of Excellence (NICoE), Bethesda, MD, USA;2. The Henry M. Jackson Foundation for the Advancement of Military Medicine, Bethesda, MD, USA;3. Section on Tissue Biophysics and Biomimetics, NICHD, National Institutes of Health, Bethesda, MD, USA;4. NorthTide Group, LLC, USA;5. National Capital Neuroimaging Consortium, Bethesda, MD, USA;1. Image Sciences Institute, University Medical Center Utrecht, Utrecht, Netherlands;2. Brigham and Women''s Hospital, Harvard Medical School, Boston, MA, USA;3. Department of Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven, Netherlands;4. Center for In Vivo Microscopy, Duke University Medical Center, Durham, NC, USA |
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| Abstract: | Estimation and testing procedures for generalized additive (interaction) models are developed. We present extensions of several existing procedures for additive models when the link is the identity. This set of methods includes estimation of all component functions and their derivatives, testing functional forms and in particular variable selection. Theorems and simulation results are presented for the fundamentally new procedures. These comprise of, in particular, the introduction of local polynomial smoothing for this kind of models and the testing, including variable selection. Our method is straightforward to implement and the simulation studies show good performance in even small data sets. |
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