Comparison of Nonparametric Regression Curves by Spline Smoothing

Abstract

In this article, procedures are proposed to test the hypothesis of equality of two or more regression functions. Tests are proposed by p-values, first under homoscedastic regression model, which are derived using fiducial method based on cubic spline interpolation. Then, we construct a test in the heteroscedastic case based on Fisher's method of combining independent tests. We study the behaviors of the tests by simulation experiments, in which comparisons with other tests are also given. The proposed tests have good performances. Finally, an application to a data set are given to illustrate the usefulness of the proposed test in practice.

Keywords:

• Comparison of regression curves
• Cubic spline interpolation
• Fiducial inference
• Nonparametric regression
• p-value

Mathematics Subject Classification:

• 62G10

Acknowledgment

We are grateful to the referee and an Associate Editor for very helpful and constructive comments that were helpful to improve our article.

This work is supported by Chinese National Natural Science Foundation with grant No. 10771015.