A method for choosing the smoothing parameter in a semi-parametric model for detecting change-points in blood flow |
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Authors: | Sung Wan Han Rickson C. Mesquita Theresa M. Busch |
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Affiliation: | 1. Department of Biostatistics and Epidemiology, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA 19104, USA;2. Institute of Physics, University of Campinas, Campinas, SP 13083-859, Brazil;3. Department of Radiation Oncology, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA 19104, USA |
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Abstract: | In a smoothing spline model with unknown change-points, the choice of the smoothing parameter strongly influences the estimation of the change-point locations and the function at the change-points. In a tumor biology example, where change-points in blood flow in response to treatment were of interest, choosing the smoothing parameter based on minimizing generalized cross-validation (GCV) gave unsatisfactory estimates of the change-points. We propose a new method, aGCV, that re-weights the residual sum of squares and generalized degrees of freedom terms from GCV. The weight is chosen to maximize the decrease in the generalized degrees of freedom as a function of the weight value, while simultaneously minimizing aGCV as a function of the smoothing parameter and the change-points. Compared with GCV, simulation studies suggest that the aGCV method yields improved estimates of the change-point and the value of the function at the change-point. |
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Keywords: | change-points smoothing spline partial spline generalized cross-validation generalized degrees of freedom |
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