SiZer Inference for Varying Coefficient Models

Abstract

Varying coefficient models are a useful statistical tool to explore dynamic patterns of a regression relationship, in which the variation features of the regression coefficients are taken as the main evidence to reflect the dynamic relationship between the response and the explanatory variables. In this study, we propose a SiZer approach as a visually diagnostic device to uncover the statistically significant features of the coefficients. This method can highlight the significant structures of the coefficients under different scales and can therefore extract relatively full information in the data. The simulation studies and real-world data analysis show that the SiZer approach performs satisfactorily in mining the significant features of the coefficients.

Keywords:

• Scale-space
• Significant features
• Simultaneous confidence intervals
• SiZer
• Varying coefficient model

2000 Mathematics Subject Classification:

• 62G08
• 62-09

Acknowledgments

This research was supported by the National Natural Science Foundation of China (No. 10971161). Zhang's work is also partially supported by the Ministry of Education in China Project of Humanities and Social Sciences (No. 12XJJC910001). We would like to thank the anonymous reviewer for his (or her) insightful comments on the earlier version of the manuscript.