A fiducial p-value approach for comparing heteroscedastic regression models

ABSTRACT

To study the equality of regression coefficients in several heteroscedastic regression models, we propose a fiducial-based test, and theoretically examine the frequency property of the proposed test. We numerically compare the performance of the proposed approach with the parametric bootstrap (PB) approach. Simulation results indicate that the fiducial approach controls the Type I error rates satisfactorily regardless of the number of regression models and sample sizes, whereas the PB approach tends to be a little of liberal in some scenarios. Finally, the proposed approach is applied to an analysis of a real dataset for illustration.

KEYWORDS:

• Fiducial inference
• Heteroscedasticity regression model
• Parametric bootstrap
• p-Value
• Type I error

MATHEMATICS SUBJECT CLASSIFICATION:

• 62F03
• 62F99

Acknowledgments

The authors thank the editor and referees for their valuable comments.

Additional information

Funding

This work was partially supported by Grant ZR2014AM019 from Shandong Provincial Natural Science Foundation of China, Grant 11171188 from National Natural Science Foundation of China, and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry of China.