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.