An efficient operator for the change point estimation in partial spline model

In bioinformatics application, the estimation of the starting and ending points of drop-down in the longitudinal data is important. One possible approach to estimate such change times is to use the partial spline model with change points. In order to use estimate change time, the minimum operator in terms of a smoothing parameter has been widely used, but we showed that the minimum operator causes large MSE of change point estimates. In this paper, we proposed the summation operator in terms of a smoothing parameter, and our simulation study showed that the summation operator gives smaller MSE for estimated change points than the minimum one. We also applied the proposed approach to the experiment data, blood flow during photodynamic cancer therapy.