SiZer map with interpolation number as the vertical axis ∗†

Abstract: A new SiZer map is constructed in this paper for exploring features of unknown regression curve. We use the number of knots m as the vertical axis for the proposed new SiZer map, which is constructed based on the p-values for testing the monotonicity of the target regression curve by spline interpolation and Fiducial infer-ence. Given different nominal levels, the corresponding SiZer maps can be constructed conveniently based on the calculated p-values, they can provide us with more helpful information in doing further statistical analysis. In order to explore more features in a given subinterval, we introduce the concept of ’sub-map ’ and construct it to make a sup-plementary analysis. Furthermore, two test procedures for testing multiple hypotheses are employed to make an improvement of the proposed SiZer map. Due to good perfor