Author details

Na Li

ESS xð Þ ; m ≜ min

accurately.

Figure 4. SiZer-RS map.

100 Topics in Splines and Applications

a 3D SiZer-RS map [47, 48].

4. Conclusion

<sup>i</sup>¼<sup>1</sup>, <sup>2</sup>, <sup>⋯</sup>, <sup>k</sup>

Nmð Þ<sup>x</sup> Gm<sup>0</sup>

Figure 4 shows that SiZer-RS map can explore the differences between regression curves

It is worth noting that, for SiZer-RS map, the coarsest smoothing level should be m ¼ q þ 1 to ensure the effectiveness of the qth regression spline and the finest smoothing level is recommend to be the one such that avg<sup>x</sup><sup>∈</sup>½ � <sup>x</sup>1;x2;⋯;xg ESS xð Þ ; <sup>m</sup> <sup>&</sup>lt; 5, where <sup>x</sup>1, x2, <sup>⋯</sup>, xg are points at which hypothesis Hm, <sup>x</sup> is tested and pixels are produced by combing different values of m. In applications, a wide range of values of mp can be used to generate a family of SiZer-RS maps. Particularly, mp and m can both be used as smoothing parameters simultaneously to construct

This chapter introduces regression spline method for testing the parametric form of nonparametric regression function in nonparametric, partial linear, and varying-coefficient models, respectively. The corresponded p-values are established based on fiducial method and spline interpolation. The test procedures on the basis of the proposed p-value are accurate in some

<sup>i</sup> Gm <sup>i</sup> ð Þ <sup>1</sup>; <sup>1</sup>; <sup>⋯</sup>; <sup>1</sup> <sup>0</sup> :

Address all correspondence to: nali@amss.ac.cn

School of Econometrics and Management, University of the Chinese Academy of Sciences, Beijing, China
