Simultaneous confidence band for the difference of regression functions of two samples

Abstract

This paper concerns the comparison of two sample non parametric regression. An asymptotically correct simultaneous confidence band (SCB) is proposed for the difference of two-sample non parametric regression functions to achieve the goal of comparison. Simulation experiments provide strong evidence that corroborates the asymptotic theory. The proposed SCB is used to analyze different samples of strata pressure data from the Bullianta Coal Mine in Erdos City, Inner Mongolia, China.

Keywords:

• B-spline
• kernel
• Brownian motion
• simultaneous confidence band
• strata pressure

Acknowledgments

The authors are grateful to Professor Jiang Yaodong’s research group at China University of Mining and Technology for providing the strata pressure data, and to two anonymous Reviewers for many helpful comments.

Additional information

Funding

This research was supported by National Natural Science Foundation of China award 11771240, 11901521 and First Class Discipline of Zhejiang-A (Zhejiang Gongshang University-Statistics).