A Method for Choosing the Smoothing Parameter in a Semi-parametric Model for Detecting Change-points in Blood Flow.
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 to 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.
Department of Biostatistics and Epidemiology, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA 19104, USA.
Sung Wan
SW
Han
Institute of Physics, University of Campinas, Campinas, SP, 13083-859, Brazil.
Rickson C
RC
Mesquita
Department of Radiation Oncology, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA 19104, USA.
Theresa M
TM
Busch
Department of Biostatistics and Epidemiology, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA 19104, USA.
Mary E
ME
Putt
Change-points; Generalized Cross Validation; Generalized Degrees of Freedom; Partial spline; Smoothing spline