Multiscale method based on spline regression for comparing multiple nonparametric curves

SiZer (SIgnificant ZERo crossing of the derivatives) is a powerful scale-space visualization technique for exploratory data analysis. In this paper a new version of SiZer based on regression spline is proposed for comparing multiple regression curves. The new SiZer is constructed on the basis of p-values for testing the equality of multiple regression functions at different locations and scales. Fiducial inference and regression spline are applied to gain the p-values. In addition, multiple testing adjustments are carried out to control the row-wise false discovery rate and family-wise error rate of the proposed SiZer, respectively. The new SiZer is more powerful even in the case of small sample size case due to the good properties of p-value and FDR control. Simulation results show that the new SiZer performs well compared with the existing SiZers. Finally, a real data example is carried out to illustrate its usage in applications.